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