I like playing as the Romans, Seluecids, and Germans.
The Romans have the best melee infantry, with their armor, and the pila. They've also got powerful cav, decent missiles, and gladiators which are made specifically to take stone walls. All three factions are ready to expand on their neighbors without worrying about their borders. I like the Brutii, because Greece is the most interesting battleground, and the Mars temples. I also like the Julii, because these guys have the best temples for law and order.
The Seluicids are the exact opposite of the Romans. They have to worry about
every border. Their territory is split into different regions. They have enemies on all sides. And that's what makes them so fun! These guys have the most interesting early game. You haven't lived until two militia hoplites side by side in a street kills about 8-10 peasants, nubian spearmen, and chariot generals without any missile support.

Their troop roster is the most interesting, with powerful catas, horse-killing phalanxes, flexible legionnaires, and oddball units like elephants and chariots.
The Germans start poor and their cities have **** growth rates. So what do you do? Take other people's lands, of course!

Spear warbands are better than the regular warbands and a wall of them make battles very simple against other barbs. When you get bigger cities, it gets really interesting. Armour-piercing chosen axemen, chosen archers, gothic cav, and of course, beserkers. Out of all the barbs, these guys are the only ones with infantry that can eat legionairy cohorts for breakfast. These guys are my favorite barb faction.