Starter system

The turntable is perfect for her. Plenty of under $75 cartridges available for it. Unless she really wants to have FM/AM (which I would doubt, she'll stream if not listening to vinyl), I'd suggest an integrated amp instead of a receiver, looking on this site and others, they go from $50 to $600, you'll get more wattage, perhaps features (like 2 tape-in's so she can stream into one of them and still have the other available) and most likely better sound/better brands then going with a receiver. 

Speakers - bookshelf or floor? Prince range? In most cases I would suggest new-fairly new rather then used/old.

If you are really trying to keep expenditure down, you might consider headphones rather than speakers. Everyone in this age range is used to listening through EarPods and headphones could be a step up. On the electronic side, you probably will get much better sound going digital streaming then an inexpensive turntable. I might ask why your daughter is into vinyl? If this is because she just likes to rotate records and produce music in a different way then an inexpensive turntable would be fine, but if this is because she’s used to listen to a high-quality system and turntable, she will come up short. so if it’s about style and lifestyle, then turn table sounds great. If it’s about the music and reproduction, then she will do much better with digital.

Thank you. Will look into integrated amps.  Headphones are a good idea as she lives in an apartment with roommates so can’t crank it up too much.  
 

I suspect she’s more about lifestyle though she tried one of those suitcase turntables and wants better than that sound wise.
 

Find a pair of Andrew Jones designed Pioneer Bookshelf speakers for around $100. You WILL thank me later.

Ok. Will look around. Thanks.