The compressor I have is a roofer's type of compressor. We called them pancake compressors when I sold them. Small tank, but larger than most airbrush compressors, good PSI regulator, but generally aimed at air nailers and the like. I have no concern about it having the 'oomph' to push the airbrush.
I think I'm reading enough to convince me to get one. Not the $50 tankless Chinese model I've seen on Amazon. I think I have seen some advertised for just the airbrush in the $75 range which is gravity fed, dual action, with reputable names that you folks have mentioned above. That, plus a $20 cleaning pot should get me started?
I use mostly acrylics currently. I have always appeased the Powers that Be by explaining to her that my paints will not kill any person or animal if they are accidentally ingested - will taste bad (I can attest by licking a brush or two in my day) but not kill anyone. I am still thinking of a booth, but maybe a homemade one. It's not the fumes that I'm really worried about with acrylics, but the overspray. If I make a homemade kit and vent it outside a window, how much am I going to see landing on my brick wall or patio? Am I being more nervous than needed as to that issue?