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