I don't know much about spraying oils but I do know a little about airbrushes. One thing I know is that you don't have to spend much for a nice airbrush.
TCP-Global is an online supplier for autobody supplies. They have an online store called Airbrush Depot. I've bought several airbrushes from them with no problems.
I highly recommend the
G233. It comes with a few different needles and tips for different viscosity finishes. It really can't be beat for the price of $49.98
Just make sure you keep it clean. wipe out the cup and lid with lacquer thinner and shoot some through it to clean it. Every once in a while, take it apart and clean thoroughly.
If you think the cup is too small, think about the
G244 which has larger cups. It's only $39.96. I've never used the G244 but I have come to trust TCP-Global and I wouldn't worry too much about the quality.
Whatever you buy, make sure you buy a "dual action" gun. This gives you much more control over a single action gun.
Whatever you use for a compressor, you'll need somewhere around 35 to 45 psi continuously. Most folks shoot at 43 to 45psi. You should be looking for a compressor with .8 cfm a water separator and a braided hose. You can get away with .6 cfm but you might run into trouble using the larger needles and caps. Don't buy a diaphram compressor, they provide pulsating air, very difficult to work with.
The TC-20T is a real nice compressor for the money and fairly quiet. Look at the site for other compressors, there's a bunch of them.
Here's your hose kit.
Good luck