First of all, do not buy compressor without air tank. Reservoir tank provides constant airflow, so you dont need to run compressor all the time. Moisture trap and pressure regulator are also an important parts of compressor. Before you buy anything read the airbrush compressor buyer's guide. You have bunch of a similar articles and guides all around web... Google it. Good luck.
More importantly in my mind, an air tank smoothes out the pressure pulses from the compressor more than just a regulator will, resulting in a less puff-puff-puffy airflow: otherwise you can get noticeable pulsations that make smooth even painting, particularly delicate painting, a bit tricky. I always prefer a large tank because it does an even better job of both holding air and maintaining a constant pressure.
