An airbrush for model builders and artists usually uses a 1/8 to 1/4 horsepower compressor. I've been using Paasche airbrushes since 1978, and bought my first compressor in 1985.

I'd REALLY need to know WHAT airbrush kit you have, but for the most part, you can use any compressor as long as you can fit adapters for the hoses, add a regulator to keep the pressure right (around 30 psi), and a water separator in humid areas.

I've used a Paasche DR500SR compressor for the last 15 years, cost was about $160
http://www.paascheairbrush.com/cgi-bin/store/search.cgi?category=Compressors+%26+Regulators