Plenty of good answers in this post, here is mine. While literally not a requirement, a decent airbrush will open doors in your hobby world you can't imagine. In my 50+ years of using airbrushes, my interest in model building has remained always at a very high level. The finish work you can turn out will amaze you, once you develope some experience and proficiency.
For me, it started out with some frustration, due to lack of ability and inferior equipment. I thought, "I'll never understand this or get it right." But in time the light started to turn on, in the cleaning process I began to understand how the components worked together, and I finally had some confidence that I could use it OK.
The I began acquiring higher performance equipment, seeing how much better my work could be really set the hook. My equipment over time ranged from low cost mediocre stuff, to higher end quite expensive items. Now I use almost exclusively Badger airbrushes, a few Paasches and one Iwata.
Probably 85-90% of my airbrushing is with a Badger 200, or 100G. Both were way under $100, closer to $60 on sale at Chicago Airbrush. Simple, durable, easy to clean and adjust, for me they're the ultimate in everyday airbrushing.
For a compressor there are endless choices, right now Harbor Freight is running a sale on two with tanks, right around $50.00, I think with pressure gages. Get a pressure regulator, very inexpensive, and you're in business.
I cannot recommend highly enough that you have a detailed look at "Don's Airbrush" website, all kinds of information on airbrushes, types, brands, etc. Also maintenance, cleaning, adjustments, compressors and all that comes with that hobby equipment. I had been doing it for many years, then learned a great deal more by cruising through his site. Well worth the time.
Karl and Plastic Junkie were right on point I think, great advice and recommendations.
I hope you'll have good luck in sorting out your choice, if you do give airbrushing a try.
Patrick