First things first: ignore everything @James
says about airbrushes!
When I asked the same question @Lovecraft0110
recommended the Badger Patriot 105. It's simple, hard-wearing and robust, pretty cheap, and while it's beginner-friendly there's also nothing stopping you from using it for high-end work. As standard it comes with a .5 needle but you can buy .3 and .7 needle/nozzle sets that are incredibly easy to swap in.
I've found mine to be very forgiving and very easy to take apart and clean - I managed to get AK primer stuck all over the place the first time I used it, and it was a very simple task to take it apart, clean and reassemble. Everything can be tightened by hand, too, so no tools are necessary.
In short, this thing is like the AK-47 of airbrushes!
One thing to keep in mind though is availability.
Despite the Patriot being an American airbrush I can find the brush and space parts for it very easily in the UK, and at reasonable prices. However while I would pay ~£100 for the airbrush, if in your country they're not so easily available and would cost you £250 and parts are difficult to come by then it's not a sound investment.
For a compressor I think that pretty much everyone I've ever come across has suggested and AS-186 or an FD-186. The letters don't seem to matter, as the 186 appears to be a generic compressor that a few different people stick their own label on.
It's not massively loud, the tank could be bigger but isn't tiny, and it does the job at a cheaper price than a lot of similar spec airbrush-branded models. Mine came with a good braided hose, and I'm fairly certain it has an inbuilt moisture trap too.
actually uses the same model, as it happens.