Yeah, bookshelf can mean a few things. I’ve got an ancient Bose Acoustimass 10* system. The bookshelf speakers are teeny, but it’s got a sub-woofer box that all of the speakers connect through. The tiny speaker set that can’t be improved by a sub-woofer is rare, especially for music. So, if you have room for one, I’d advise getting a speaker system with one and amp that supports it, if you go that route.
If you are looking to buy an amp and speakers, you can eat up that budget with a really nice dedicated amplifier quickly. If you want one with terrestrial radio, you can get not quite as nice a sound quality, but you usually get a more flexible head unit. I’d advise that, myself. You can get an Onkyo TX-8220 for $199, and I’d imagine it’d make you mostly happy. It’s a decent brand, they sound plenty nice the last time I heard one. For $100 more you can get a Yamaha R-N303, which apparently supports all kinds of streaming services itself. I can’t vouch for their interfaces or anything, but I do still love the sound of the Yamaha A/V receiver I’ve had for 20 years, and it’s certainly held up. If I have one complaint about the receiver, it could have a better phonograph preamp. But that’s a small complaint for a receiver being sold at that time, and probably not a concern for you.
If you’re dead set against a sub-woofer, then get speakers that can reach to the low end. The most reasonably priced speakers I can see that reach below 40Hz (20Hz is around the lower limit of human hearing) are something like the Polk Audio S20.
So, even on the high end, you’ve got some space left on your budget. Grab a CD player. Don’t buy an expensive one, just get one with the features you want that seems durable. I don’t really have advice, here. I got a 60 disc CD changer at the same time as I got the Yamaha receiver and the Bose speakers. It lasted until 2013 or so, then died. After we finally put all the CDs back into their holders, we used my 1987 vintage Tascam deck until around last year, when it croaked. Now we’re using my wife’s 1990 or so vintage JVC. It’s holding up. (Looks at Cruchfield’s home CD players) Good Lord! You can go into that much debt over a CD player these days? You’re on your own here. They all should sound pretty much the same, try not to spend more than $200.
*Yeah, they’re supposed to kind of suck. I won them at work 20 years ago and have never seen a reason to replace them. I wouldn’t really advise buying them though, they are pricey for what they are. I may add an additional external sub since my amp supports it…but I haven’t yet.