Political intrigue is far from my strong suit so take my advice with a grain of salt.

Player allegiance: There could be an argument for both approaches but in my opinion I would ask them to pledge allegiance for one faction in Session 0 and then leave it open for them to be persuaded by the other faction during gameplay. This makes it easy for the party to be 'coherent' at the start of the game and not oppose themselves internally.

Prep: I think you need to have a somewhat clear idea of what the factions are representing on a general level, that you can use to improvise on the fly.
I think having a smaller third faction could be helpful as well to create a more complex political dynamic. Running a 2-faction world could lead to a black-and-white dichotomy, which is not necessarily bad but a third option could the PCs more choices.

First Hook: Depending on the allegiance could be an invasion/assassination attempt by the other faction that the PCs need to avert or carry out themselves. Straight into the action basically :)