Final Fantasy XIII/Weapons

 Each character has access to eight different weapons which can be acquired through fight spoils, item spheres or shops. Each weapon can be upgraded twice with various components—the first upgrade is to a more powerful version and the second is the final ultimate version of the weapon. To upgrade a weapon to its intermediate form, you'll need to max its level, then find the appropriate catalyst. For the ultimate form, all weapons use the Trapezohedron catalyst after you've maxed their levels.

Lightning
Lightning's weapons all balance their advantages with serious disadvantages, so make sure you choose the right weapon for the job. Although Organyx has great stats, the Leadenstrike and Ironstrike properties make her much slower, greatly reducing any benefit you might get from them. This can be counteracted somewhat by Haste and speed accessories, but if you're using her as a Ravager, it's far more important to get the stagger bar up quickly, which is easier with other weapons. The Hauteclaire is right behind, but also comes with a major drawback, the Stagger Lock property, which doesn't let you get stagger enemies. Unless you're using Lightning as a Commando, avoid this weapon as well. If you want to have Lightning be a Ravager to take advantage of her great abilities, including Army of One, you'll want to choose between Blazefire Sabre, your starting weapon with great stats but no special property and a useless synthesis group, and the Lionheart, which has worse stats, but the great Quick Stagger property and the Gestalt synthesis group for when she's leading the party.

Blazefire Sabre

 * Found: Starting weapon
 * Property: None
 * Synthesis group: Physical defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 2,000

Axis Blade

 * Found: Item sphere in Palumpolum, ../Chapter 7/
 * Property: ATB Charge → ATB Charge II
 * Synthesis group: Boost
 * Catalyst: Adamantite
 * Shop: Plautus's Workshop
 * Cost: 15,000

Edged Carbine

 * Found: Item sphere in the Gapra Whitewood, ../Chapter 5/
 * Property: None
 * Synthesis group: Magic defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 4,600

Lifesaber

 * Found: Item sphere when you first get to The Palamecia, ../Chapter 9/
 * Property: Improved Raise → Improved Raise II
 * Synthesis group: Low HP
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 20,000

Gladius

 * Found: Item sphere at the beginning of the Pulse Vestige, ../Chapter 2/
 * Property: None
 * Synthesis group: Physical defense
 * Catalyst: Uraninite
 * Shop: Up in Arms
 * Cost: 7,100

Organyx

 * Found: Shop only
 * Property: Leaderstrike → Ironstrike
 * Synthesis group: Adamancy
 * Catalyst: Cobaltite
 * Shop: Gilgamesh, Inc.
 * Cost: 280,000

Hauteclaire

 * Found: Item sphere in Mah'habara, ../Chapter 11/
 * Property: Stagger Lock
 * Synthesis group: Gestalt
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 20,000

Lionheart

 * Found: The first item sphere in Eden, ../Chapter 12/
 * Property: Quick Stagger
 * Synthesis group: Gestalt
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 28,000

Sazh
Sazh has some interesting weapons, with some giving huge magic or strength stats at the cost of zero in the other stat. Sazh is recommended as a support character, so if you plan on using him in a variety of ways (such as Synergist and Ravager), you're not going to want to limit yourself to one stat in particular. Your starting weapon, the Vega 42s, and the later acquired Rigels both give nice, even advancement for both magic and strength, although the Rigels have higher max values and the very nice Gestalt synthesis group. The Rigels outperforms all other weapons in strength except the strength-only Pleiades Hi-Powers, and outperforms all other weapons in magic, except for the Deneb Duellers and Aldebarans, which have severely less strength or no strength at all, respectively. The problem with Rigels is its Stagger Lock property, which won't allow Sazh to induce staggers on enemies. If you plan to use Sazh as perhaps the single Ravager in a paradigm, you're going to want to go with a different weapon. Although the stats are much lower, another good choice for a balanced weapon are the Antares Deluxes, which have the great Chain Bonus Boost property and belong to the Boost synthesis group, making it a fantastic weapon for Ravagers, while still proving decent magic for Synergists.

Vega 42s

 * Found: Starting Weapon
 * Property: None
 * Synthesis group: Magic Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 2,000

Spica Defenders

 * Found: Item sphere in Nautilus, ../Chapter 8/
 * Property: Augment Maintenance → Augment Maintenance II
 * Synthesis group: Positive Effect
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 14,500

Deneb Duellers

 * Found: Item sphere in Lake Bresha right after leaving Snow, ../Chapter 3/
 * Property: None
 * Synthesis group: Magic Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 3,900

Rigels

 * Found: Item sphere in the first room with the two Berserkers in the Fifth Ark, ../Chapter 10/
 * Property: Stagger Lock
 * Synthesis group: Gestalt
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 19,000

Aldebarans

 * Found: Shop only
 * Property: Leadenstrike → Ironstrike
 * Synthesis group: Adamancy
 * Catalyst: Cobaltite
 * Shop: Gilgamesh, Inc.
 * Cost: 263,000

Pleiades Hi-Powers

 * Found: Item sphere in the deserted schoolhouse in Oerba, ../Chapter 11/
 * Property: Paper Tiger → Silk Tiger
 * Synthesis group: Damage Reduction
 * Catalyst: Perovskite
 * Shop: Gilgamesh, Inc.
 * Cost: 22,000

Antares Deluxes

 * Found: Item sphere by a save point before you get to Leviathan Plaza (where the Juggernauts are), ../Chapter 12/
 * Property: Chain Bonus Boost → Chain Bonus Boost II
 * Synthesis group: Boost
 * Catalyst: Uraninite
 * Shop: Plautus's Workshop
 * Cost: 11,000

Procyons

 * Found: Third item sphere along the path at the Sunleth Waterscape, beginning of ../Chapter 6/
 * Property: Stagger Maintenance → Stagger Maintenance II
 * Synthesis group: Gestalt
 * Catalyst: Dark Matter
 * Shop: Plautus' Workshop
 * Cost: 30,000

Hope
Hope's weapons are mainly geared towards magical use, and that should be your deciding factor, as he can't learn any of the "strike" Ravager abilities even if you wanted to make that his primary role. Hope is going to be fairly worthless in aggressive roles, so there's really no reason to go with a high-strength weapon, unless you're attempting to put together the Ultimate Physic synthesis ability for him, where he can take no physical damage. Although the Malphas looks tempting with its very high, balanced stats, unlike Snow, Hope doesn't have the HP to counteract the Paper Tiger and Silk Tiger properties of that weapon. Hope's best weapon comes down to whether you're using him as your main Synergist or not. If so, the Vidofnir's good magic and buff-enhancing property and synthesis group are unmatched. However, if Hope will be your Medic and Ravager when he's not healing, Otshirvani will make him much quicker, especially when attacking a staggered enemy. In the early game, take advantage of the Hawkeye's greater magic and Magic Defense synthesis group before its lack of special property makes one of the other weapons more appealing later on.

Airwing

 * Found: Starting Weapon
 * Property: Critical: Shield → Critical: Shield II
 * Synthesis group: Low HP
 * Catalyst: Uraninite
 * Shop: Plautus's Workshop
 * Cost: 10,000

Hawkeye

 * Found: Second item sphere in the Gapra Whitewood shortly after the save point following the Vespid fight, ../Chapter 5/
 * Property: None
 * Synthesis group: Magic Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 4,400

Otshirvani

 * Found: Second item sphere after leaving the Skywalk in Eden, guarded by a Proto-behemoth, ../Chapter 12/
 * Property: Siphon Boost → Siphon Boost II
 * Synthesis group: Boost
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 28,200

Ninurta

 * Found: Third item sphere in the Vile Peaks, ../Chapter 4/
 * Property: None
 * Synthesis group: Physical Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 2,800

Vidofnir

 * Found: Item sphere at the end of a rail not long before fighting the Ushumgal Subjugator in Palumpolum, ../Chapter 7/.
 * Property: Defense Maintenance → Defense Maintenance II
 * Synthesis group: Positive Effect
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 16,900

Simurgh

 * Found: Item sphere at the entrance to the Third Tier in Taejin's Tower, ../Chapter 11/.
 * Property: Stifled Magic → Fettered Magic
 * Synthesis group: Ultimate Physic
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 21,200

Malphas

 * Found: Shop only
 * Property: Paper Tiger → Silk Tiger
 * Synthesis group: Damage Reduction
 * Catalyst: Perovskite
 * Shop: Gilgamesh, Inc.
 * Cost: 198,000

Alicanto

 * Found: Second item sphere in the Fifth Ark after the first room with the two Behemoths, ../Chapter 10/.
 * Property: Stagger Lock
 * Synthesis group: Gestalt
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 18,000

Vanille
Vanille has very high magic, low strength and HP, and no access to "strike" Ravager abilities, so, like Hope, you'll want a weapon with a high magic stat rather than strength. You get the Pearlwing Staff fairly early, so that's a good weapon to start with, and if you take it all the way to its ultimate form, it will reward you with the highest magic of any of her weapons, though it doesn't have a special property and its synthesis group is worthless later in the game. Mistilteinn, Belladonna Wand and Heavenly Axis are almost identical stat-wise, but the Belladonna Wand has a property for better debuffing, while the others are fairly useless or come with a downside (Stagger Lock). If you're concentrating more on being a Medic than Saboteur, the Healer's Staff will boost your efficiency in that area. Don't be fooled by the Tigerclaw's great stats—you'll be attacking very slowly with the Leadenstrike and Ironstrike properties, and you won't be doing enough damage to make the Adamancy synthesis group's ability useful either.

Binding Rod

 * Found: Starting weapon
 * Property: None
 * Synthesis group: Physical Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 2,500

Tigerclaw

 * Found: Shop only
 * Property: Leadenstrike → Ironstrike
 * Synthesis group: Adamancy
 * Catalyst: Cobaltite
 * Shop: Gilgamesh, Inc.
 * Cost: 300,000

Healer's Staff

 * Found: Item sphere on the series of cutbacks leading up to the Midlight Reaper in Nautilus, ../Chapter 8/
 * Property: Improved Cure → Improved Cure II
 * Synthesis group: High HP
 * Catalyst: Adamantite
 * Shop: Plautus's Workshop
 * Cost: 19,800

Pearlwing Staff

 * Found: First item sphere in Lake Bresha, ../Chapter 3/
 * Property: None
 * Synthesis group: Magic Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 2,300

Rod of Thorns

 * Found: On a raised mound with two Gorgonopsids near the entrance to The Archylte Steppe, ../Chapter 11/
 * Property: None
 * Synthesis group: Magic Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 3,000

Mistilteinn

 * Found: Item sphere near a save point in the long hallway after the Juggernauts in Eden, ../Chapter 12/
 * Property: Ally KO: Power Surge → Ally KO: Power Surge II
 * Synthesis group: Low HP
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 11,000

Belladonna Wand

 * Found: The second item sphere in the Sunleth Waterscape, ../Chapter 6/
 * Property: Improved Debuffing → Improved Debuffing II
 * Synthesis group: Positive Effect
 * Catalyst: Uraninite
 * Shop: Plautus's Workshop
 * Cost: 31,200

Heavenly Axis

 * Found: Item sphere in Oerba outside the destroyed house, ../Chapter 11/
 * Property: Stagger Lock
 * Synthesis group: Gestalt
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 24,000

Snow
The weapon you choose for Snow mainly depends on the role he'll be playing. The Sacrificial Circle gives awesome strength and magic stats at the price of a large hit to your HP. This is really only beneficial if you plan to use Snow as an attacker instead of or as well as a Sentinel, as the weapon essentially trades some of his very high HP for attack power though the Paper Tiger and Silk Tiger properties. If you will be using Snow solely as a Sentinel, the Umbra is a better choice, as you will retain your HP and get the Improved Ward property which will reduce damage to your teammates. Your starting weapon is a good all-arounder in the beginning, but once you decide on your role, you should switch to one of the others. The only other weapon to note is the Feymark, which has a very high magic stat and no strength is used for extremely specific fights where you might need its Ultimate Magic synthesis group.

Wild Bear

 * Found: Starting weapon
 * Property: None
 * Synthesis group: Physical Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 1,800

Paladin

 * Found: Second item sphere after the Nutriculture Complex in Palumpolum, ../Chapter 7/
 * Property: Improved Guard → Improved Guard II
 * Synthesis group: High HP
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 20,000

Rebel Heart

 * Found: First item sphere after leaving the Skywalk in the beginning of Eden, ../Chapter 12/
 * Property: Critical: Power Surge → Critical: Power Surge II
 * Synthesis group: Low HP
 * Catalyst: Uraninite
 * Shop: Plautus's Workshop
 * Cost: 11,000

Power Circle

 * Found: Starting weapon
 * Property: None
 * Synthesis group: Physical Defense
 * Catalyst: Scarletite
 * Shop: Up in Arms
 * Cost: 4,500

Feymark

 * Found: Item sphere in one of the hallways between the large open spaces and rooms where enemies come out of the walls in the Fifth Ark, ../Chapter 10/
 * Property: Enfeeblement → Hindrance
 * Synthesis group: Ultimate Magic
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 25,000

Sacrificial Circle

 * Found: Shop only
 * Property: Paper Tiger → Silk Tiger
 * Synthesis group: Damage Reduction
 * Catalyst: Scarletite
 * Shop: Gilgamesh, Inc.
 * Cost: 210,000

Unsetting Sun

 * Found: Item sphere in the Sixth Tier of Taejin's Tower at the elevator from the Fifth Tier, ../Chapter 11/
 * Property: Stagger Lock
 * Synthesis group: Gestalt
 * Catalyst: Perovskite
 * Shop: Gilgamesh, Inc.
 * Cost: 21,000

Umbra

 * Found: Item sphere on one of the right-hand platforms in the large room with extendable walkways before the fight with Barthandelus on The Palamecia, ../Chapter 9/
 * Property: Improved Ward → Improved Ward II
 * Synthesis group: Magic Defense
 * Catalyst: Adamantite
 * Shop: Plautus's Workshop
 * Cost: 32,600

Fang
Since Fang has the highest potential strength of any character, you'll want to capitalize on that with a high-strength weapon for the most part. Your starting weapon is good on strength, although you'll want to switch up later in the game when better synthesis groups or properties are available. If Fang is more of a Commando, Taming Pole offers the best all around stats and is part of the powerful Gestalt synthesis group. Its drawback is the Stagger Lock property, but this is mitigated for Commandos, who are not the primary enemy staggerers, like Ravagers are. If she will be doing more Sentinel duties, Gae Bolg will improve her counter significantly. Because she has access to area-of-effect Saboteur abilities like Slowga, Fogga, Painga and Cursega, the Pandoran Spear offers improved debuffing while also providing high strength and great magic. Fang also has access to both the Ultimate Physic and Ultimate Magic synthesis group abilities, with Dragonhorn and Shamanic Spear, respectively.

Bladed Lance

 * Found: Starting weapon
 * Property: None
 * Synthesis group: Physical Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 4,500

Dragoon Lance

 * Found: Shop only
 * Property: Stifled Magic → Fettered Magic
 * Synthesis group: Ultimate Physic
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 230,000

Partisan

 * Found: The item sphere on the way from Base Camp to Hope in Vallis Media, beginning of ../Chapter 11/
 * Property: None
 * Synthesis group: Magic Defense
 * Catalyst: Perovskite
 * Shop: Up in Arms
 * Cost: 6,600

Shamanic Spear

 * Found: One of the item spheres in the Tesseracts of Orphan's Cradle, ../Chapter 13/
 * Property: Enfeeblement → Hindrance
 * Synthesis group: Ultimate Magic
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 31,000

Punisher

 * Found: Item sphere near the Adamanchelid in Eden, ../Chapter 12/
 * Property: Stagger: TP Charge → Stagger: TP Charge II
 * Synthesis group: Magic Defense
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 31,000

Pandoran Spear

 * Found: Last item sphere before entering the Rotary Shaft (large circular room with concentric walkways) on The Palamecia, ../Chapter 9/
 * Property: Improved Debilitation → Improved Debilitation II
 * Synthesis group: Positive Effect
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 16,200

Taming Pole

 * Found: Item sphere guarded by a Vetala on the bridge after Oerba, ../Chapter 11/
 * Property: Stagger Lock
 * Synthesis group: Gestalt
 * Catalyst: Uraninite
 * Shop: Gilgamesh, Inc.
 * Cost: 27,000

Gae Bolg

 * Found: Item sphere found by Fang and Lightning on their way to help Hope in Palumpolum, ../Chapter 7/
 * Property: Improved Counter → Improved Counter II
 * Synthesis group: Positive Effect
 * Catalyst: Scarletite
 * Shop: Plautus's Workshop
 * Cost: 13,100