When choosing compressor you should consider if it will be able to constantly Air Compressor For Laser Cutting china provide desired pressure and volume of air. Small airbrush compressors little compressors boast amazing pressure figures but actually poor flow rates adequate only for airbrush pistols. Even if small compressor would be able to 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 want to do is engrave, although also then we got significant smoke traces around engraved picture.
it was rated for volume of 
~2.4cfm and had a 1 gallon tank which may be filled to 58 PSI. It managed to give us continuous 1 bar (14 PSI) of pressure, nonetheless it had to operate all the time and overheat badly within five 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) without fear of overheating since compressor engine is not on all the time. Using reserve surroundings in tank we are able to also drive up to 3.5bar (50psi) for brief jobs.
The best setup for me would be compressor rated to >6cfm, huge 70+ gallons tank rated to 10bar (140psi) and software air control via solenoid valve.