Compressor is fairly easy.
Generic AS186 compressor. They're under $100 $90 on Amazon in the USA.
As for the airbrushes, I'm not an expert, but went down this path a couple years ago. I started with a cheap no-name airbrush to slap primer, varnish and basecoats down, but not a whole lot more. It worked pretty okay, had a decent feature set (came with .2, .3 and .5 nozzle and needles, full cleaning kit, quick detach and a hose) and I got enough mileage out of it to be happy. I then bought an Iwata Eclipse HP-CS as my "Nice Airbrush" and its been in use when I didn't want to swap out nozzles on the cheap one. Really happy with the HP-CS, with one downside: The HP-CS doesn't have a limiter so you've got to nail down your brush control to use it with precision. Its definitely capable of such precision. More recently, with some money to burn, I decided to buy a Harder & Steenbeck Infiniity CR+. I haven't used this as much, but the jump in quality from the Iwata HP-CS to the H&S wasn't as expected; the H&S trigger seems more "vague" than the HP-CS. If I could get that Iwata trigger feel with the feature set of the H&S, I think I'd be most happy. However, I'm sure I'll just learn to deal with it.
As for "breaking" them, that might be a concern, but if you have to frequently disassemble them, either for cleaning/clogs, or for changing out needles/nozzles you may lose a part or they might break as you over-torque the nozzle into the body. With the cheap no-name ones, getting replacement parts is a crap-shoot as the sellers are "here today, gone tomorrow" from Amazon. I'm looking for a brand I can get parts for. Iwata, H&S, Badger, others, are backed up by market presence.
What really encouraged me for more airbrush use was the ease of cleaning. The Iwata and the H&S have very decent openings from the top to get mine scrubbed/rinsed out for the next color. The no-name brands off Amazon are all over the place, but I did find one that is just as easy to clean as my Iwata. I do use that beater brush for priming and varnishing, since it lives with that 0.5mm nozzle.
So, on my bench, I've got two brushes used most often, my (second) beater $40 brush for priming and varnishing, and the Iwata Eclipse HP-CS for most of my actual "work." The H&S will get some more use, but I just haven't owned it long enough to make any real personal opinions (other than my initial impressions comparing it with the $170 Iwata). I really dislike the "Buy once, Cry Once" as all of these brushes I have, exhibit some strong points and have their own unique shortcomings.
edit: the 2nd beater airbrush was purchased because the 1st one, I broke a nozzle, was able to find replacement parts, but the 2nd one was just infinitely easier to clean (wider channel where the cup meets the needle), and it just blasts through primer and varnish.
How much are you looking to spend?
The most important thing is to get a decent compressor. The AS 186 https://www.amazon.com/Timbertech-Airbrush-Compressor-Professional-Automatic/dp/B07VT3RV47 is pretty much the standard from the research I did when I first started.
After that you need a hose. The one I got was this. It's got a 1/8 fitting which connects to the compressor. Then you just need to make sure you get an airbrush with a 1/8 fitting as well.
https://www.amazon.com/gp/product/B002FDX36I/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
Then in terms of airbrushes there's a whooooole slew of different ranges from the very cheap to very expensive. There's nothing wrong with starting out with a cheaper airbrush at first for priming, base coating, and varnishing. Any of the cheaper airbrushes on Amazon would work for that. But if you want something more fitting for someone who actually wants to get into airbrushing for real, the Iwata Eclipse HP is usually the one I see people recommend.
Though I went with a 90 dollar Badger Patriot 105 myself, which I like. It just required an extra adapter in order to use it with that hose. (Badger has its own stupid proprietary thread size).
Finally you need Airbrush Cleaner and Flow Improver/Thinner. A little cleaning pot also is nice to have.