Selecting a first airbrush and compressor is confusing. The compressor is easier - pick one that you can afford, provides sufficient adjustable air flow/pressure and is of good quality and have at it. Because most airbrushes function similarly choice IMHO is really a personal thing. All airbrushes will spray paint but if the one you have doesn't feel right, has a trigger location not suited to you, has too broad or too fine of a nozzle/needle or you don't enjoy using etc then using it will be a chore. Iwata, Badger, Paasche, Harder & Steenbeck, Grex and others all make fine airbrushes and all spray paint well - the differences are in physical build and ergonomics. The choice of single action or double action - either will do what the other will but I think DA a little more convenient but if only one airbrush SA might be a little easier to learn. Ease of cleaning is important and, for me, I like an AB that has an easily removable (and large enough to handle) nozzle. My Badger Sotar, for example, is a really nice AB but the nozzle is so tiny that I fear loosing it each time I clean the AB so it doesn't get cleaned as often as it should. Similarly, screw in nozzles are not well suited to repeated on/off cycles. Ease of cleaning also relates to suction or gravity feed - for me gravity feed is much easier than having to clean a bottle but, again that's personal. The above links are worth checking and have some very useful information.
My personal favorites: A Sparmax TC620X compressor, an H&S Evolution Silverline AB
Others here have their own favorites and I'm not a fanboy of any particular one. The one you use and like is the best.