Considering playing this with the girlfriend, but not much of an MMO guy and not sure how to choose our classes so we don't end up split up and unable to play together for large chunks of the game.

I've seen lots of jokes with WoW about Horde vs. Alliance so I assume going Republic vs. Empire is meaningful in the time we will be able to play together? Should we both go Republic or Empire? Same or different classes? If we choose different classes will that mean little to no quest cross over that we can help each other out on?

Both go Rep or Emp, then pick different classes. The starting areas for the classes are split with Imp Agent and bounty hunter starting in the same area and the two sith start in the same as well. Probably split like that on the Republic side too.

Definitely choose different classes, so you have a wider range of combat options. As crazyleaves says, there are two different starting locations for each side, so you'll have to choose a set that starts together. One of you playing as a Sith Warrior or Jedi Knight while the other plays as a Sith Inquisitor or Jedi Consular respectively would work well. I don't know about the other classes abilities.

Yeah go with the same side. Also make sure you both join the same server.