When choosing compressor you should consider if it can constantly provide desired pressure and level of air. Little airbrush compressors small compressors boast amazing pressure figures but Air Compressor For Laser Cutting actually poor flow rates sufficient limited to airbrush pistols. Even if small compressor can push enough air it’ll likely overheat in short while.
Our laser cutter was included with small membrane pump (Smallest upon 
the picture), I really do not know what specifications it has but stream of air was extremely weak. It is enough if all you want to do is engrave, although even then we got significant smoke traces around engraved picture.
it had been 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 run constantly and overheat badly within five minutes.
Third and current compressor we got was 6cfm rated belt driven device with 13 gallon container which is filled to ~100psi. With this unit we are able to run at continuous ~2bar (31psi) without fear of overheating since compressor engine isn’t on at all times. Using reserve air in tank we are able to also press up to 3.5bar (50psi) for short jobs.
The best setup for me will be compressor rated to >6cfm, huge 70+ gallons tank rated to 10bar (140psi) and software air control via solenoid valve.