Brian,
I have a Craftsman 3-gallon, 125 psi compressor that I've been using with my airbrush (an older Testor's single-action). I don't have any kind of water trap/separator attached (tho I know I should and have been lucky so far) to my system. So far, a 3-gallon has been just fine. Don't expect to get a LOT of airbrush time on your compressor without it "firing up" and refilling. 3-gallons is just not that much. To wit:
The FIRST time I used it was a 3-color camo scheme on my JagdPanther. The base color went on (and, yes, I was "startled" by the compressor kicking in)(THAT should have learned me!!) and when I started the next color, all was well.....then, BRRRRRRRRRR! Needless to say, I had to redo that part.....got startled, airbrush went up, and camo pattern was jacked. Lesson learned: My compressor is now in another room with a 50-foot hose attached! And, most airbrushes come with an adapter that is compatible with a 3/8" fitting (a male end is attached to my brushe's hose). Quick connects ARE A MUST!!! Makes life SO much easier!!
That little "doo-dad" that Ken shows attached to his set up is just what you need (me too

). If you get a "moisture" trap, attach it semi-permanent. I'd be surprised if you will ever need to remove it.....the worst enemy to an air tool is water sucked out of the tank (condensation) and into the tool. Another tip; when you are done with your compressor, DRAIN IT!!! And, leave the drain valve open until the next time. After a few times, you might be surprised at how much condensation comes out.
Last thing, IF you have a problem locating a trap, let me know via PM, I can get you one easy enough.
HTH,
Mike (++) (++)