I have a few ideas but I don't know how well they work, because I haven't played much with Persia. Here are the ideas, though.
1. Tradition > Liberty. Yes, Liberty has a guaranteed GA that jives with the timing of the UU, but I don't think you're going to reliably get to Civil Service (or finish liberty) fast enough to get Itza with your liberty GE if you are going wide and warmongering. Maybe I'm wrong about this and I'd love to hear from a better player, but I don't think I could do it.
If you finish Tradition and NC with two or three cities, you might be able to get Itza and you'll certainly be teched up enough to build an army that can take the city that builds it (unless on another continent).
1.b. Immortals are badly timed for the kind of game that will work with the other bonuses, so just use them for defense and CS quests, not being too ambitious.
1.c. Don't attack everyone. Target the player(s) with good wonders and annex their capitol(s). You especially want Notre Dame (and Itza, obviously).
2. Aesthetics has a policy that will give you a ton of culture since you're maximizing happiness, so you probably want that and the +25% artists opener even if you're not going CV.
3. The Order ideology will probably be best, since the AIs lean heavily toward it almost all the time. You want to stay super happy, so shared ideologies are important. However, in that rare game where there's at least a little ideological pressure for Freedom, or you have so much culture it doesn't matter what anyone else thinks, go for Freedom! That +50% to GA in tier two would be amazing.
4. Unlike most civs, you have a military bonus that isn't locked into a particular era. It's a flexible, powerful advantage to be able to time a GA to help knock out whatever AI is threatening to win the game.
It seems to me that Persia has a lot of different little edges. Any one of them by itself is not game changing, but taken as a whole this civ seems stronger than when I first started writing this post. They seem well-suited for a muscular culture victory. I think I've talked myself into playing them next...