When choosing compressor you should consider if it will be able to constantly provide desired pressure and level of air. Little Air Compressor For Laser Cutting china airbrush compressors small compressors boast impressive pressure figures but actually poor flow rates sufficient only for airbrush pistols. Also if small compressor would be able to push enough air it’ll likely overheat in couple of minutes.
Our laser cutter was included with little membrane pump (Smallest upon the picture), I really do not know very well what specifications it has but blast of air was extremely weak. It is sufficient if all you have to to do is engrave, although even then we got substantial smoke traces around engraved picture.
it was rated for level of ~2.4cfm and had a 1 gallon container which can be filled to 58 PSI. It managed to give us constant 1 bar (14 PSI) of pressure, nonetheless it had to operate all the time 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 continuous ~2bar (31psi) without fear of overheating since compressor engine is not on continuously. Using reserve surroundings in tank we are able to also push up to 3.5bar (50psi) for brief jobs.
The best setup for me will be compressor rated to >6cfm, large 70+ gallons tank rated to 10bar (140psi) and software air control via solenoid valve.
