All of my links are to Chicago Airbrush which is a pretty decent online retailer.
Before you buy please spend the time and watch this video. It will really educate you about airbrushes.
http://www.youtube.com/watch?v=tsW-v...layer_embedded
1. What type of compressor works best? Is there a quiet version of it for indoor use? What price point are we talking? First unless you spend in the $800-$1500 range there is no such thing as a silent or quiet air compressor. This what I use a Paasche D3000 and it isn't as loud as my washer, dryer, or dishwasher. A solid compressor that can handle 5-50 PSI effortlessly which is all you need for an airbrush. look to spend on this between $100 and $400.
2. What type of airbrush and why? What is the price point, roughly? Other than the Chinese knockoffs, which are garbage, most airbrushes are fairly close in quality. I own two Paassche brushes. Both are siphon feeds one that is a bottom feeder and one that is a side feeder. Bottom feeds are good if you need to lay down quantity of paint. Gravity feeds are about detail. Side feeds are the meeting in between these two points. I'll be buying a gravity feed soon because I want the finer control but my side feed is a champion.
3. What type of paint should be used? Can I still use acryllic or should I be using something else? evilhomer pretty well covered it. Only two things should be used to thin acrylic paint: distilled water and airbrush medium. Windex will destroy the metal over time and alcohol will lead to more clogs because of tip dry.
4. What stages of the process do you recommend using them for? Is there an airbrush/compressor that is better suited for all stages of the process? Lester Bursley is a great reference for seeing what you can do with a brush. Here is a great example. Also Rob over on Spikey bits has some good videos. For the second part you need a compressor that can handle 5-50 PSI, and at minimum a side feed siphon. However, I would go with a gravity feed. Probably a Badger Krome or Patriot, or a Paasche Talon.
Feel free to drop me a line with any other questions.