I'm quite familiar with Karl's (the Doog) work and stand in awe of his talent.
He uses a Badger 150 siphon fed airbrush, which is the airbrush I started with before I bought my 100LG gravity feed. I had the same compressor, as well, which worked pretty well. Mine didn't have an auto shut off valve, and so I upgraded my compressor a few years ago and bought a 3 gallon "pancake" 100psi compressor from the local hardware store.
Depending on the hose, you may need an adapter to reduce it down to fit most vinyl hoses. My Badger braided hose has the correct size (1/4" NPT) end to attach directly to my compressor, though I use an air pressure regulator to control the air flow, and that is what the airbrush connects to. Same fitting! I know people who use even larger compressors. The airbrush doesn't care, as long as the air is dry and oil free. And it's actually the paint that cares about the oil!
I chose the "garage" style compressor to appease SWMBO (She Who Must Be Obeyed), as I can also use it to pump up our bike tires and run a pneumatic nailer. A multi-tasker is better for my use than a uni-tasker!