Well, I guess I'll try to give what advice I've got:
In my experience, start with a cheaper airbrush, then move up in price/quality with your painting abilities. If you're also like me though, I try to do things right the first time and just get a quality airbrush so I don't have to stress the issue later. Badger is a good brand, or Pasche (spelling?).
When mixing paints for an airbrush (if its not airbrush paint), mix the paints to about a milk consistency (slightly thicker than water). Takes practice. Too thin, no coverage and runs off the model. Too thick, and it just doesn't spray.
Some people use rubbing alchohol, windex, and/or water as paint thinners to help it go through an airbrush and spread onto the miniatures properly (breakage of surface tension in the paint).
Imo, I try to do things as professionally as possible, so I use an actual paint thinner. Get something that matches the type of paint (acrylic paint, etc)
Along with thinners, try to do a little research on something called "tip dry." It's when the paint on the end of the airbrush nozzle dries, and clogs the tip, sometimes causing disastrous splatters and such. To avoid this, research a paint retarder for the brand of paint you plan on using (lengthens the amount of time it takes for the paint to dry. I hear good things about Tamaya, but I personally don't use a retarder). Usually a very potent stuff, so take caution.
With all things, airbrushing itself takes practice and time. Try to use it similar to using a spray-paint can. Back and forth motions, from a variable distance (I usually go around 6 inches) in nice smooth strokes (remember a good follow through!). Too far from the model and the paint gets chalky looking, and actually dries before it touches the model. Too close and the paint globs. Too slow while passing and you glob the paint on (loss of detail, cracking paint). Too fast and the paint goes on too thin and you get no coverage. Practice
Multiple light coats is better than 1 heavy coat.
Air supply is a usual issue. You can either go with an airbrush compressor (small, quiet, but a bit expensive) or a normal compressor (I got a little 1 gallon pancake air compressor from walmart for $50). Another common alternative is a portable air tank. Get air at a gas station or something, and bring it home. No compressor. Some people use canned air, but usually run into the issue of a short life span of the pressure, and the cans are a bit pricey.
You will need a good airbrushing environment. Good ventilation (garage, shed, etc.). Try to do some research as well on an airbrush booth, which pulls the air (with paint molecules) into the booth and outside, away from you and your lungs. I also suggest wearing a dust mask whilst painting, just to be safe.
I'm pretty sure that's about all the information my nerdy little brain has to offer at the moment. If I come up with more information, I'll let ya know. And I can guarantee that other people are far more knowledgeable in the topic than myself.
Best of luck, there are so many possibilities for painting when you get the hang of things.
