When choosing compressor you need to consider if it will be able to constantly provide desired pressure and level of air. Small airbrush compressors little compressors boast impressive pressure figures but actually poor flow rates sufficient only for airbrush pistols. Even if small compressor would be able to push enough air it’ll likely overheat in couple of minutes.
Our laser cutter came with little membrane pump (Smallest on the picture), I Air Compressor For Laser Cutting really do not know very well what specifications it has but blast of air was extremely weak. It is sufficient if all you want to accomplish is engrave, although actually then we got significant smoke traces around engraved picture.
it was rated for level of ~2.4cfm and had a 1 gallon tank which may be filled to 58 PSI. It managed to give us constant 1 bar (14 PSI) of pressure, nonetheless it had to operate on a regular basis and overheat badly within 5 minutes.
Third and current compressor we got was 6cfm rated belt driven unit with 13 gallon tank which is filled to ~100psi. With this unit we can run at constant ~2bar (31psi) without fear of overheating since compressor engine isn’t on all the time. Using reserve atmosphere in tank we can also force up to 3.5bar (50psi) for short jobs.
The best setup in my opinion would be compressor rated to >6cfm, large 70+ gallons tank rated to 10bar (140psi) and software air control via 
solenoid valve.
