When choosing compressor you should consider if it will be able to constantly provide desired pressure and level of air. Small airbrush compressors small compressors boast amazing pressure figures but actually poor flow rates enough only for airbrush pistols. Even if small compressor would be able to push enough air it will likely overheat in couple of minutes.

Our laser cutter came with little membrane pump (Smallest on the picture), I really do not know what specifications it has but blast of air was very weak. It is sufficient if all you want to do is Air Compressor For Laser Cutting engrave, although actually then we got substantial smoke traces around engraved picture.

it had been rated for volume of ~2.4cfm and had a 1 gallon tank which can be filled to 58 PSI. It were able to give us constant 1 bar (14 PSI) of pressure, but it had to run constantly 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 are able to run at constant ~2bar (31psi) without concern with overheating since compressor engine is not on at all times. Using reserve surroundings in tank we can also push up to 3.5bar (50psi) for short jobs.

The best setup for me would be compressor rated to >6cfm, large 70+ gallons tank rated to 10bar (140psi) and software air control via solenoid valve.