I used a tankless airbrush compressor for several years and it worked OK but there are advantages to a more powerful compressor with an air tank, if your painting environment is OK with the noise and the size. Tool compressors are cheaper per PSI, develop higher pressure, turn on less often, and the air tank buffers the air supply to your airbrush to eliminate the pulsing that small "instant ON" airbrush compressors tend to have. The bigger the compressor and its air tank, the less often it will run. Right now, I'm using a Porter Cable 2hp 135 psi compressor with a 6 gallon air tank, which I "liberated" from one of my sons. I added a pressure regulator and a moisture trap (about $40 total). It sits comfortably under the work bench where I paint crankbaits. You have to decide where you will paint, how much equipment will fit the space, how much noise is too much, and how much you want to spend for your setup. IMO, at the minimum, you want a compressor that is rated for 60 psi max pressure. This will run an airbrush at a sustained pressure of around 45 psi, which is the maximum pressure that most of us ever use (actually, most of us shoot at lower pressures than that, 10-35 psi, but you want more pressure there when you need it).
Also JMHO, the sweet spot for airbrushes is one with a tip diameter of .3 to .35mm. If you use only one airbrush, that tip size will shoot just about any airbrush paint and do a good job of it. Some airbrush companies like Badger or Paasche don't state their tip sizes. If you want to use one of their models, simply know that their tips are typically larger than those found on airbrushes from the Far East, of which Iwata is the best known. Personally, I use an Iwata Revolution B with a .3mm tip and it would be my choice if I were going to use one airbrush. It sells for around $75, which I feel is a bargain price for such a high quality airbrush.