So, you don't know what faction to pick do you? Well, this is dependent on your style of game play, but here are a few suggestions.
Julii, Brutii, Scipii
These three first factions are actually pretty good in cavalry and extremely well in infantry. For example, the cohorts are a great backbone of an army and can hold the line very well in battle. My favorite unit is the Arcani. These bad boys can hide anywhere and are a very good attacking and have an even better defense with two hitpoints like a general. Although not much of a head on fighter, these units can pick off units in secrecy, and might be able to turn the tide of battle. The economy of these factions is good if you make trade routes with other factions. The only annoying thing is the Senate mission message that you get time to time. If you don't want to do them like me, then just skip them, but you can't get more popularity with the Senate.
Seleucia
Seleucia is one of my favorite factions. The phalanx based units can easily support your main armies for even the longest of battles. They also have Silver Shield Legionaries, which are the closest thing to a Roman Legionaries. Cataphracts rule the battle field in this faction. They are heavy cavalry (and oh boy are the heavy) and can turn the tide of any battle in one or two charges. They're also pretty cool looking; they are covered in a shiny metal skin. You start out near the Egyptians near Jerusalem. You start with five cities, I think. If memory serves, the Numidians and Egyptians will create war, while Parthia will want to make alliances, and treaties.
Carthage
Carthage is pretty much like Seleucia. They have elephants which can trample through any enemy line, but be careful! They will rampage over ALL units on the field if they get spooked. You can remedy this by selecting the unit card and selecting the special ability of driving a sword into the elephant's neck, killing the elephant and ending the rampage. Watch out for the Roman factions, they will want to start taking over your cities, especially Lilybaeum, the one next to the Brutii city on the island.
Well there you go. You can use these factions is you beat the game on the long campaign with a Roman faction. Using phalanx formations like 300 are pretty fun to mess around with when you have like 2000+ peasants coming at you.
