The first question often asked is if an inexpensive, relatively low capacity air compressor purchased at your local tire store, or big box store, or even work properly for air brush painting? If so, what are the issues with them?
The most significant issue is, I think, noise. Good quality air brush air compressors run fairly quietly. A "cheapie" air compressor does not!
Regardless of what compressor you use, as long as it's got the air flow your paint apparatus / gun requires (CFM) at the air pressure you need (PSI), and the air is of sufficient quality, then that unit will work for you.
Having excess capacity means that you can handle the more viscous paints, as you'll have lots of air in reserve!
Here are some things to consider when looking for a compressor to excel in supplying compressed air for air brush painting.
One of the most important hallmarks of an air brush type compressor is that it's quiet. It can cycle on with almost no sound, and cycle off with a gentle "psssssht" as the unloader valve dumps air from the compressor head cylinder.
That quietness doesn't come cheap. Depending on the size you pick, you might not get much change from a $1,000.00. Silence is golden, and it costs a lot of gold!
As a result of that high cost for a quiet compressor, we'd be inclined to purchase the $200-or-less compressor from the tire store, spend another couple of hundred building a soundproof box around the darn thing, and put the rest of the money we saved from not buying a "quiet" compressor in the bank!
When you do that, make sure you leave good air access for supply air and to allow cooling of the compressor head.
The downside of this decision is that oil-less compressors usually cost more, they are often quite a bit noisier than the oil-lubed comparable units, and they tend to run hotter which, unless the hot compressed air is mediated via "air preparation", will have some negatives as to compressed air quality. (See this link for more information about water problems in your air). A hotter running compressor usually means more maintenance and shorter compressor life, too.
Instead of buying into an oil-less compressor, simply ensure that the air that exits the lower cost, oil-lubed compressor, is adequately filtered to remove free water and oil. Please see here for detailed information about compressed air filters in general, and here for information on filters that remove oil from the air.
If you are using a lot of compressed air, say a quite large piece of work, it's likely that the water vapor exiting your compressor receiver will condense in your air line or your gun, leading to water droplets projecting onto your work.
That being the case, you can add a "point-of-use" dryer to ensure that no water can reach your work. Have a look at this page for information about dryers.
Using a precision regulator means that you can "dial in" the correct pressure that works best with your gun and your paint mix, and since they are so much more sensitive than general purpose units, the precision regulator will ensure that flow is consistent and steady.
When I asked for details, it boiled down to the fact that the user did not understand that all compressors are not designed for continuous operation, and the compressors that they were purchasing were definitely not! Their lack of knowledge about 'duty cycle' did them in.
Take a look at this page for more information on air compressor duty cycle, and do make sure that the compressor you purchase has enough flow capacity, at the pressure you need, so that it can rest as often as necessary to ensure long life.
Don't forget to drain the receiver regularly to eliminate free water from the reservoir, and also remember that the liquid you drain is now considered a hazardous waste as it contains water and oil, and should be disposed of properly.
Good luck with your airbrush compressor hunt!