I use a Craftsman 4 gal pancake air compressor. Yes, it's loud when it starts up but it's in the basement and not really heard throughout the house.
It can get down to the 3-5 psi range and can top out at 120 psi. I usually airbrush in the 20 psi range and have great results. With the tank, you don't have any pulsation and the low airbrushing pressures allow a long time before the compressor kicks in.
I decided to get a general air compressor so I could use it for other things than just airbrushing. It's been great for cleaning dust out of the computer and other stuff around the house.
Karl