well, it is entirely up to yourself on what you build,
Thermal Baths: is possibly the most popular, becuase of the extra population you get, which means you can build more troops and navy
Library: is not used really, it gives you extra 12 points in the academy
Lighthouse: the 2nd most popular i believe, it gives your naval units a speed boost
Theatre: this building lets you run plays to give you Culture Points it costs 10k wood, 12k stone and 10k silver to run a play
i believe it depends on what kind of city you are building, a LS nuke you could use Lighthouse so your LS move faster or else Thermal Baths to build more LS
Troops nukes you tend to use Thermal Baths because you can fit over 1k slingers, 100LS and a few catapults