Families and talents
One third of the talents available to you depend on the family you pick. This is the only real difference among the families, but it is not at all insignificant!
Valerii
The Valerii's most powerful talent, and it comes along quite early, is their ability to get 5% interest on the city treasury. There is no cap, and it is not at all unusual to see treasuries above 100,000 denarii (far more than you could ever need) if the scenario drags on long enough. (However, you must exercise caution: you will pay 5% interest if you're in the red.) With even a modest source of income from trade or temples, any monetary concerns are likely to disappear very quickly. Their extra trade routes are also quite handy.
They do have one talent that you may find entirely useless: you can get a bonus of 15,000 denarii 30 minutes into the game. (You know when 30 minutes have passed when your city enters the Ancient city state.) Thanks to your 5% interest, you are likely to already have far more denarii than you could possibly know what to do with by that point in the game. Still, if you take a lot of time to think without pausing the game, it could come in handy.
Buildings
Houses
Should you build an insula, an equites house, or a villa? Well, it depends on what you want the house to do. You should never build a house without a purpose in mind (unless it's to meet a "build N houses" scenario objective), because they provide no value other than the resources they produce and the job openings they fill. Thus, usually you should decide what buildings you want and build the houses to match. For example, if you know that in a certain area you want a wheat farm, a pig farm, a prefecture, and a Temple of Mars, build two insulae, an equites house, and a patrician's villa (assuming you want the bonus from using a patrician; otherwise build another equites house). This way you will not build more houses than you need. Having more houses than you need is not particularly harmful, but it wastes money and also upkeep materials (though insulae and equites houses don't require upkeep at all if near a prefecture -- but equites will still consume goods and patricians will still consume olive oil). It will also lead to the Unemployment city state if your employment falls under 50% for too long.
Forum
The forum is very large, but provides no benefit to surrounding buildings. Thus, despite supposedly being the heart of the city, you will want to build your forum somewhere where it won't get in your way. You can always move the forum if it gets in your way, but it will cost you 5 popularity, and, if you don't have the appropriate character talent, 1000 denarii.
Prefecture
If you are running low on building materials, consider building a prefecture in a neighborhood that doesn't have one. This will reduce the upkeep costs of the buildings you already have there, which may significantly increase the supply. Prefectures are also handy for handling criminals and putting out fires, but this is a much smaller concern since a well-defended, properly managed city should never have these problems.
Herbalist shop
Herbalist shops are not particularly useful. Fountains are generally sufficient to prevent the plague unless you're playing for a very long time.
Temples
The Temple of Vesta is the least useful temple. The denarii donated to it are not placed in your treasury directly, and while you can take the money anyway, it costs popularity. The Temple of Mars gives the same amount of religion happiness and does give you the denarii directly, so if you have a choice between Vesta and Mars, go with Mars if you can.
Theater and bathhouse
Theaters and bathhouses are likely too big to be worth it, unless you are absolutely sure you will not need the space. (If you do want an entertainment building that takes up a comparable amount of space, you may want to consider a Colosseum.) Arenas, odeums, and taverns are good alternatives. If you will need to provide high entertainment to a large number of citizens, you may also consider building the Circus Maximus somewhere where it will be out of the way, since it will increase your entertainment percentage by 20 on the entire map.
Tax office
The tax office is too expensive to be worth the trouble most of the time. It will take a long time to recoup the cost (likely at least ten minutes) unless your city is large, and if your city is large you're unlikely to have a cash problem in the first place. Building more temples in populated areas or establishing more trade routes are more likely to generate good income for much cheaper. If you can get one for half price due to a Golden Age, however, it may be worth a look. If you get a large research bonus from character talents and can research the tax office quickly, it's also worth considering making it one of your first five buildings if you get them for free.
By the way, the same applies to gold mine upgrades. Upgrading a mine once may be a good idea, especially if you can get it for half price due to the Efficiency city state. More than that, though, and it will likely take too long to recoup the cost of the upgrade. (For example, if you pay 500 denarii to add 50 more denarii per minute, it will take 10 minutes just to make up the cost. That's a big investment for a mere 50 denarii per minute.)
Library and philosopher's academy
Libraries and Philosopher's Academies are only useful if your research output is low. Usually you will not need many techs and so building them may be a waste of time.
Senate
The Senate is only useful if you use Authority actions often or if you want to use the more expensive ones.
Pantheon
The Pantheon can be useful if you need high religious satisfaction, since temples and villas take up quite a bit of space. If you don't need high religious satisfaction, then don't worry about it.
Artisans' market
Artisans' markets are most useful in scenarios where you have to produce or export a large number of goods. They are usually not needed otherwise because insulae with sufficient food satisfaction will produce goods on their own. Note that artisans' markets also provide food satisfaction, so despite their large size they provide decent value for the space.
Colosseum
The Colosseum may not be particularly useful. It will provide 100% entertainment to everyone near it, but it is such a huge building and its range only extends so far, plus it's so expensive. You can generate 100% entertainment with a few buildings in a smaller space (though, aside from an arena, you will have to have people, most likely equites or patricians, staffing those buildings), especially if you build the Circus Maximus, which, though larger, can be built out of the way and benefits your entire city.
When your first five buildings are free
If you get your first five buildings for free due to character talents, consider using them on expensive buildings such as these if you're sure you will need them:
- Victory column
- Circus Maximus
- Colosseum
- Barracks
- Tax office (you will need the tech first, but if you have a very high research rate from character talents, it may not take long to research)
Note that one of your first four buildings will have to be a forum. You can use two of your other three free buildings to get an insula and, say, a trading post in order to get building materials if you need them for your fifth building. For some of these you will likely need an estate to provide the rest. Of course, a trading post may be more useful if you have free trading routes from the appropriate character talents.
No workers?
Sometimes nobody is working at a building because, even though you have enough houses in the area, the only unemployed houses of the required type are out of range. To solve this, try clicking on the building and clicking "Start work". This will usually fix the problem by rearranging your workers.
Military
Walls
Walls are essential if there is a chance you will not be able to defend your city with military units. They are also useful as a distraction; enemy units will often keep attacking your walls, getting slaughtered by your towers, even if they can just walk around them or through a hole in the wall. If you have enough stone and denarii, you may even want to build a second layer of walls so that any enemy troops will take massive losses from your towers if they try to attack your city. Naturally, this would also be excellent for stalling them long enough to bring in troops. Be aware, though, that walls are not an effective defense against catapults. For those, you will need troops.
Choice of units
Do not underestimate the power of hastati! Experienced hastati can still be pretty strong, and several experienced hastati units throwing pila can demoralize or even destroy an entire enemy squad in one shot. Especially if you have a time limit, it may be sufficient to simply build as many hastati as you can. Hastati are especially nice for dealing with time limits because they can train all the way up to level 8 fairly quickly when near a military camp.
If you don't have enough iron but want more troops, you have two options. The obvious one is to import it. If you don't want to, or can't, however, you can choose auxilia. They will still require resources, but they may be resources you have easier access to, such as wine.
If you want to win without losing a squad, secutores are a good bet, but they take a long time to train to level 8.
Miscellaneous
You may want to build a Victory Column so you can train your units to level 8 instead of level 4. If you get your first five buildings for free, consider making it your fifth building. (Don't make it one of your first through fourth).
Allied military camps do nothing for your own squads. If you want a boost to training speed or to replenish your units, build your own camp.