When choosing compressor you should 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 can push enough air it will likely overheat in short while.
Our laser cutter came with little membrane pump (Smallest upon the picture), I really do not know very well what specifications it has but stream of air was very weak. It is adequate if all you have to to accomplish is engrave, although even then we got substantial smoke traces around engraved picture.
it had been rated for level of ~2.4cfm and had a 1 gallon tank which may be filled to 58 PSI. It were able to give us constant 1 bar (14 PSI) of pressure, nonetheless it had to run at all times 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) Air Compressor For Laser Cutting china without fear of overheating since compressor engine isn’t on at all times. Using reserve air flow in tank we are able to also drive up to 3.5bar (50psi) for short 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.