Okay, I have some experience with these. In some cases, you'll want more than one, especially if she really gets into it. It can be hard, have you seen some of the work? Wow.
Anyway, start with these two:
External mix. (a Badger may do okay here for a while, Paasche has one too). They're cheaper and do larger volumes and can cover larger areas.
Internal mix, dual action. Paasche. Here you want something that's dual action and uses multiple size needles (for changing spray, maintenance and easier to change when it wears out). They'll have the threaded screw and lock nuts on the end of the handle usually. You want something that takes color cups and you'll want several color cups. Maybe a jar filled with water (or solvent but most airbrush artists use water based paints for safety) to clean between cups. This allows fast changes between colors, what an artist needs.
Later on you may want to also get another Paasche, it has a small color cup built into the airbrush. It does very fine detail. The other one above though should do much of what it can do, so it'll be up to your daughter if she finds a need for this later.
The air compressors, yeah, the small ones made for it work well but a larger one from Home Depot would be better. It shouldn't run TOO much because the airbrush doesn't bleed much air from those tanks so it won't be running all the time. The DeWalt model that looks like a donut? Probably a good one to consider --if serious. You can also run tools from it, so not a total loss. Make SURE to use a water trap! No matter what compressor you go with, USE the water trap! It's mandatory with airbrushes. You don't want oil or water in the lines.
Maintenance of airbrushes is the big turn off. They can be tedious to clean and the needles can be damaged if paint is left to dry on them (hard to get off without harming the needle). So she'll have to be dedicated to cleaning in between, not letting them sit for long and then total cleaning at the end of the session. Sometimes they need cleaning during a session, depending.
Me? I stick with oils and brushes when I paint now! Even quality oils and quality brushes and good canvas and frames are cheaper than airbrush setups. But I still like airbrush art, like I said, some of it is simply amazing. I could never get into it --I used 'em to paint models as a kid, was really into that, and I used 'em to Duracoat a rifle and shotgun before Cerakote became available. Sold the airbrush, Cerakoted the rifle and the Duracoat black has actually held up on the shotgun (oh, and a Glock!) surprisingly well, forgot they were Duracoated until right now.
So it has it's uses. If you get a sandblast cabinet and a bigger compressor, you can run all sorts of stuff and just run a line with a water trap into her studio space and call it good. You'd be able to use her external feed rig to Cerakote your own rifles then! Save money, get more out of it and make it pay for itself that way!
Good luck, I wish I knew more but I do know that much. Things may have changed and she may have ideas on what airbrushes to go with. But certainly a decent external feed and a quality internal feed, dual action with interchangeable needles and color cups. Don't cheap out, the Badger 350 is as cheap as you want to go for an external mix but I'd stick with all Paasche for a beginner --even if she progresses and gets into it, years later she'll still be using them for something.
