Not all airbrush compressors run quietly. Most any compressor will power an airbrush since the operating pressures are so low (usually less than 30psi and often less than 20psi).
Large compressors can run an airbrush for a while before they need to recharge the tank, so the noise is not constant. Also, larger compressors with large tanks can be plumbed remotely, if you have the space.
One suggestion is to place the pressure regulator as close to the airbrush as is practical for the greatest control. I have mine at the union between the airbrush hose and the compressor line (on larger spray guns I place the regulator right on the inlet for the gun). This helps to ensure that the pressure at the airbrush is what you set and allows for pressure loss is the line between the compressor and the tool.
If you choose to use a moisture trap, it will be most effective if placed far enough down-line from the compressor to allow any moisture in the line to cool and condense.
I hope this helps.