When choosing compressor you have to consider if it can constantly provide desired pressure and volume of air. Small airbrush compressors small compressors boast impressive pressure figures but really poor flow rates Air Compressor For Laser Cutting china enough only for airbrush pistols. Also if small compressor would be able to push enough air it'll likely overheat in short while.
Our laser cutter was included with little membrane pump (Smallest upon the picture), I do not know what specifications it has but stream of air 
was very weak. It is sufficient if all you have to to accomplish is engrave, although also then we got substantial smoke traces around engraved picture.
it was rated for level of ~2.4cfm and had a 1 gallon container which may be filled to 58 PSI. It managed to give us constant 1 bar (14 PSI) of pressure, but 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 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 continuously. Using reserve atmosphere in tank we are able to also drive up to 3.5bar (50psi) for brief jobs.
The best setup for me will be compressor rated to >6cfm, large 70+ gallons tank rated to 10bar (140psi) and software air control via solenoid valve.
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