What type of compressor are you looking at? There are generally two types; the "General Purpose" compressors and those made specifically for airbrushing. The former usually have a higher capacity, highre pressure, are noisier, and cost less. The airbrush compressors are normally very quiet, have enough volume and pressure for an airbrush, and cost quite a bit more. You have to pay for silence
In general, avoid diaphragm compressors since they frequently have a pulsation in the airflow unless they have a tank to eliminate it. MikeV can give you more info on that.
Regardless, you'll need a hose, regulator and moisture trap. These can be purchased separately, but the regulator will normally come with the compressor. You'll also need to make sure the compressor will fit your airbrush hose. Most compressors typically have a 1/4" NPT connection, and most airbrush hoses will fit this connection although an adapter is sometimes required.