When choosing compressor you should consider if it will be able to constantly provide desired Air Compressor For Laser Cutting pressure and level of air. Little airbrush compressors small compressors boast amazing pressure figures but actually poor flow rates sufficient limited to airbrush pistols. Also if small compressor would be able to push enough air it will likely overheat in short while.
Our laser cutter came with little membrane pump (Smallest upon the picture), I do not know very well what specifications it has but blast of air was very weak. It is enough if all you want to accomplish is engrave, although also then we got considerable smoke traces around engraved picture.
it had been rated for volume 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, but it had to operate at all times and overheat badly within 5 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 fear of overheating since compressor engine isn’t on continuously. Using reserve surroundings in tank we can also drive up to 3.5bar (50psi) for short jobs.
The best setup for me will be compressor rated to >6cfm, huge 70+ gallons tank rated to 10bar (140psi) and software air control via solenoid valve.