I have always opted for a compressor with a tank for my airbrushing setups. The tank acts as a buffer between the airbrush and compressor. The airbrush can withdraw ample CFM that the compressor cannot maintain on its own. Short sessions, allow the compressor to keep the tank topped off is best.
My first compressor was/is (it makes too much noise so it is used only in the garage now) a 3/4hp with a 3 gallon tank. It gets used to run mechanics air tools too! My primary indoor model shop only is a Paasche D3000. It has no problems with pushing air through any of my airbrushes including my VLs with the largest needle and nozzle.
I've always been one to use 'MORE PRESSURE', usually up anywhere around 38psi, but of late I have been cranking the pressure down to 11-15psi. Two noticable things happened. Much less overspray and fogging up of the paintbooth. Better control! Plus after spending hours masking, the pressure from the airbrush isn't lifting off the tape either!