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 "Omega" version of the weapon. To upgrade a weapon, you'll need to max its level, then find the appropriate component to use as a catalyst to transform the weapon into the next version.

Lightning
Organyx has the highest potential overall, with the best Max Strength and Max Magic. However, it is only obtainable at a very high price from a shop, with no chance of getting it from an enemy drop, mission or item sphere. Although both the Gladius and Edged Carbine feature highly in Strength and Magic, respectively, they are weak in the opposite attribute. The next best all-around weapon after Organyx is Hauteclaire, which can be obtained from an item sphere in Mah'habara in ../Chapter 11/. Until then, they're all relatively the same at their minimum levels, and you shouldn't worry too much about upgrading them until you're in a position to grind fairly efficiently so you can quickly upgrade your weapon of choice as cheaply as possible. Just look at how your stats will be affected at the equip screen when you find a new weapon, and make your decision based on which is best suited for the primary role you've chosen for Lightning.

Blazefire Sabre

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

Axis Blade

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

Edged Carbine

 * First 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

 * First 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' Workshop
 * Cost: 20,000

Gladius

 * First 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

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

Hauteclaire

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

Lionheart

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