When choosing compressor you need to consider if it will be able to constantly provide desired Air Compressor For Laser Cutting china pressure and volume of air. Little airbrush compressors small compressors boast impressive pressure figures but actually poor flow rates enough only for airbrush pistols. Actually if small compressor can push enough air it will likely overheat in short while.
Our laser cutter came with little membrane pump (Smallest on the picture), I do not know what specifications it has but stream of air was very weak. It is adequate if all you want to accomplish is engrave, although actually then we got considerable smoke traces around engraved picture.
it had been rated for level of ~2.4cfm and had a 1 gallon container which can be filled to 58 PSI. It managed to give us continuous 1 bar (14 PSI) of pressure, nonetheless it had to operate at all times and overheat badly within five minutes.
Third and current compressor we got was 6cfm rated belt driven device with 13 gallon container which is filled to ~100psi. With this unit we can run at continuous ~2bar (31psi) without concern with overheating since compressor engine is not on continuously. Using reserve atmosphere in tank we can also drive 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.