I use two GMC brand ones sold in the Bunnings hardware stores in Brisbane, Australia, there should be a local similar cheap unit on your side of the world.
The GMC one is 40 litre tank and it runs up to 120 psi, then bleeds down to a kick in pressure of about 80 psi. I have not airbrushed with it yet, but it runs my rattle gun for the car pretty well. The unit I have has two outlets that can be used, one direct from the tank and the other after the built in regulator. I use the direct outlet to run my air tools and the regulated will be used for airbrushing.
If I want to get a bit more tank reserve, and a bit more grunt, then I connect the second compressor via the direct connection and use a T piece in that line to power the air tools. Just buy the ends and join them to a home made one metre long air line. One of the compressors cuts in before the other, but it is less than 5 pounds of difference, and it works just as happily without any further adjustment. This suits me as the compressors can fit in the back of my wagon with the wheels on, and the capacity of both units together is great. Just needs two power points. Still, remember that you are doing this as a hobby, you are not a tyre store and these little compressors will run fairly quietly compared to bigger units. If you want to reduce the noise from your compressor, then add an extra filter to the air inlet. Even just a big piece of foam tied around it will help. (Not over the cooling fan for the motor stupid!)
You can also use the cheap reserve tank of a truck tyre and a T piece with the one compressor. This might give you enough pressure to paint for longer before getting up to restart the compressor. If you use an extension cord and have a plug at your feet, you can control when the compressor starts and you won't get a nasty surprise while painting that fine detail.......
These small compressors work well for household work and will run most things. Spray painting a full scale car would be slow, but doing a bonnet and waiting a couple of minutes halfway through to let the compressor catch up is not a problem. I expect my airbrush will be happy and work well, as it doesn't use as much air as a car sized gun. It sould give me a good run and I'll have to try it soon......
Hope the ideas help, Peter