First off, remember that the AI civs are going to do everything twice as fast as before. They can now build, grow, and research as fast as you can, so you might be in for a little bit of a shock. Also, every citizen after the second will be unhappy, so you'll need to make greater use of the luxury slider than before.
It might be best not to bother with wonders at first; in the early game, shields and turns are better spent on workers, settlers, units, and some improvements than on wonders. What'll help you more: the Great Wall, or 10 settlers? Once you've expanded and built up your military and infrastructure, a few wonders might be helpful. In the Middle Ages, Leo's Workshop is probably the best, followed by Sun Tzu's, then the science wonders and maybe Bach's (but only if you can't get enough luxuries). That assumes you plan to do a fair bit of warmongering, of course.
The AI's favorite government type affects diplomacy a little bit. Basically, if you and the AI are in the same gov other than their favorite, you get a small diplomatic bonus; if you're both in the AI's favorite gov, you get a large bonus; and if you're in the AI's least favorite gov, and the AI's not, you get a large penalty. I ignore that and stay in Republic myself. Republic is a good government to stay in, though since you're playing vanilla, you might want to revolt to democracy later if you're religious. Then again, maybe not--you have to research two optional techs to get it.
As for civs, you really can't go wrong with the three that civverguy suggested, but if you want to fight a lot, you might try China or the Iroquois, both of which have excellent unique units. Now if you were playing Conquests, the Iroquois would probably be the best choice since they have a far stronger trait combo than in vanilla or PTW.