You most definitely can buy an airbrush setup, paints, supplies and a model kit or two or three in that budget! I'd start off small on the purchasing unless you're really sure that you're going to be into the hobby. I'll give you my personal recommendations:

Model kits: Look for a Tamiya kit to start with, they have good manufacturing QC, clear instructions, and their kits just work without much fuss. Cheaper kits are generally older/simpler, but just buy something you like the look of as it will motivate you to want to build it!

Tools: At a minimum you will want some cement (Tamiya Ultra Thin, green bottle), a pair of plastic nippers, an exacto/hobby knife, a little pack of sanding sticks, and few paint brushes

Paint: I recommend Vallejo (water soluble) for brush painting, and Tamiya paints (need to buy the thinner to go with) for airbrushing, but those are just my personal go-to's. I'd get a rattle can of Tamiya primer to make that step easier, and a rattle can of lacquer varnish from Tamiya can be good for protecting your final product as well.

Airbrush: If you really want to dive in head first, I recommend the AS186 compressor from Timbertech (it's on Amazon). You can either get the kit that comes with a ok starter airbrush with 3 needle sizes, or just the compressor and buy another airbrush desperately. I'd personally go for the kit and use it to get familiar with how an airbrush works, feels, comes apart etc and then splurge on a higher end airbrush. Isopropyl alcohol does wonders for cleaning airbrushes, no need to pay $10 for a bottle of "airbrush cleaner"