With the amp, what are you going for? Clarity or volume? I ask because I've noticed that the stock HU in the Fit is very weak, and worse, very noisy. The problem with that is if you amplify from the stock HU, the noise will only be worse. I'm sure plenty of people have done it and don't mind, and you may not mind, but it is something worth pointing out. So if clarity is important, you will have to upgrade the HU. If not, then no biggie!
About the Infitity speakers: be prepared for problems with clearance. I've installed a number of different Infinity model speakers, and there is almost always a problem with the speakers being way too deep for the door. The only times there isn't a problem is if it is a large SUV or truck. You will certainly have to purchase at least 3/4 inch speaker spacers to put them in.
Rear subs in door: Honestly, you really won't notice any difference from 6.5 inch dedicated subwoofers. These are bascially just standard door speakers that are only 1-way (vs 2 or 3 way). Also, more problems with clearance as they tend to have larger magnets. In my opinion, you should put 4 of the same speakers in the doors, put a 4 channel amp behind them (start with the stock HU and see how you like it) and see what it does for you. You may end up wanting to put a small sub into it. JL makes a great stealth sub that is self-powered and looks stock.
Components: I'm not bothering with components in the front as I don't want to cut my doors. There are some component speaker sets out there that have mounting options using a bracket (pretty sure Rockford does), but that usually involves a few screw holes, or glue if you're okay with them falling off all the time.
(Sorry for the long post, I tend to go overboard!)