I use a Paasche VL airbrush its quite old probably from the early 70's I'm guessing, I got it from my dad, he doe some crazy airbrushing on cars. I used to use it alot when i built model cars.
Its old but its very nice and adjustable. I have the original metal paint cup and I was able to get a much larger 6oz bottle that attaches to the bottom. There still sold on Ebay for good price too, I've seen complete ones with the tools, cups and tips in the original case for less than $40. You can also still get all the parts as it was and still is very popular.
For an air compressor you only need a small 1cyl air compressor, they make special ones that only have a 1gal tank because they don't consume much air. I use a small 10gal 110v single cylinder compressor that came from an old brewery, its probably 50 years old. The key is a good regulator and water/oil separator, especially on piston driven compressors.
Make sure the airbrush is clean clean clean! Also if your going to use water based paint do not use tap water because the minerals and additives in city/well water will contaminate the paint, so use distilled water in a jug from the grocery store. Safety is important, paint and solvents are obviously bad for your health good ventilation and a respirator. Also get a gallon milk jug and cut the top off so when you clean your airbrush you spray your solvents/paint it will go in that.
For practicing stroke and spray patterns, instead of wasting paint and having to clean your airbrush, buy what's called "brush-up paper", its a specially coated paper that when its spray it with water it turns black on the paper, the best part is when the paper dries out the black goes away and you can use it over and over again its awesome!
One of the cool things that you can do for beginning is to use stencils, you can draw or trace a pattern on a manilla folder and cut it out and use it over and over again, its great when you want to have the same pattern and shape on opposite side of an object you cant have side by side.
I hope this helps out a bit. Ill go through my photos and look for some stuff my dad or myself have done. It takes practice, practice practice, but its great fun and if you get good at it you can make some good money on the side!