1 - At least 12awg straight to the battery. 10awg would offer more headroom. Don't forget to fuse your power line!
2 & 3 - Any amp will work. It all depends on what you want out of your audio system and your budget. I suggest going to a local car stereo shop that has a good reputation (not BestBuy!) and asking some questions.
Let them know what you intend to do, your budget and they should be able to help you out.