Airbrush:
dual action, internal mix, gravity feed. These are all musts for this hobby. Additional needles are nice for different projects.
Personally I use a Paasche Talon which meets all of the requirements. It can be found on Ebay for around $80-90.
Compressor:
4-40 psi, regulator, water trap, air tank is optional but nice if noise is an issue.
I have this compressor and it is quiet as a whisper.
http://www.harborfreight.com/1-8-eighth-hp-40-psi-oilless-airbrush-compressor-93657.html