Just about any air compressor with a pressure regulator will work just fine for airbrushing. A nice pretty silent compressor marketed as a airbrush compressor is nice but not necessary. Home Depot, Eagle Hardware most lumber yards sell commercial type compressors that will work just fine. Check the compressors out at one of the above mentioned stores ,ask to hear the compressors run. For a limited budget you might want to check out Co2 tank as air source.
Tanks are quite ,clean and provide dry air.
One 15 pound tank will give you about 20 to 30 hours of air depending of course on the air pressure you run. Not the best way to go if shirts is what you will be airbrushing because of the high PSI required. Check your local welding supply or beverage supply company for rental prices. Compressed air cans is another way to go if your thinking short term. You'd find this very expensive long term.