I hesitated to reply to this thread because there are so many things to cover depending on your level of knowledge with both cars and electrical systems in them. To answer your questions:
1: For your budget stick to amps in the 100-200 dollar range. Stay away from wal-mart brand amps.
2: Speakers are rated by power handling, freq. response just like any speaker. For door speakers, you want a 2-way. In this instance Sony makes great budget friendly speakers.
3: Speaker wire will depend on if you amplify your door speakers. If you just run them off the head unit high level out, factory wire works. For a sub, I recommend 12 gauge. Rocketfish brand is fine.
4: Wire kits can simplify things for install. If your going to have a pro do it, he will deal with that. If your doing it yourself, I would recommend buying wire/cables separately. Mainly because most amp kits do not have large enough gauge wire in them.
5: No you do not need a capacitor. Some of the biggest competition setups don't use capacitors. There's reasons for this. Unless you're going to run 1000w mono's to two 15's, you don't need it. Even then, an alternator with a higher output capacity is what you would need.
6: Sound deadener works, but for what it's intended to do. Most people think dynamat for example, is used to keep things from vibrating. Although it sometimes does this, the mat is used to add mass. This helps keep sound waves from resonating in enclosed compartments such as trunks and doors. For the most part I wouldn't worry about it, again budget.
Each of these areas can be explored in more detail, frankly, it would be a book. The most important element in making car audio sound good, even with budget components, is proper install and wiring. I sent you a p.m. with my contact number if you wish to discuss it further.
Crutchfield offers quality gear on a budget. Check em' out.
