First, I suggest you do an extensive search of this portion of the forum. There's a ton of information on the subject, and it seems that someone asks similar questions quite frequently.
Airbrushing is half technology and two thirds art—just do the math…
Two very basic tips:
Learn how to disassemble and clean the thing without damaging it. Airbrushes are precision instruments, and they have delicate parts. Practice taking it apart and putting it back together. Work over a resilient surface so that when you drop something, there's less chance of damage.
Practice, practice, practice. Then practice some more. The learning curve is steep at first, but stick with it. After twenty years of experience, you'll still be learning.
Recommendations: Double action—Thayer & Chandler Omni 4000. Single action—Paasche H. A double action is a little harder to start on, but not enough so to remove it from consideration. The main advantage of the Paasche H is that its parts are a little harder to damage while cleaning. These are my two personal choices, (I own one of each.) and I'm sure others will chime in with as good or better ones (Mike V, paging Mike V and other airbrush gurus. You are needed in the Painting and Airbrush section!)
I also recommend that you start with acrylics, because that simplifies cleaning enormously.
Responding to Ben: Yes, Thayer and Chandler is now owned by Badger and are available from Bear-Air and Dixie Art, as well as direct.