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