Can a $750 system sound good?

Yes, it can be done ...

I once had a bedroom system that consisted of a Fisher 500 receiver that I bought at a garage sale. A Radio Shack 5-disc CD player. A pair of N. E. A. R. speakers. Stands for the speakers. And hooked up with Radio Shack wire.

Cost for the entire system?

Receiver = $65.00

CD Player = $200.00

Speakers = $400.00 (traded a preamp straight across for the speakers. I paid $200 for the preamp).

Stands = $100.00. They were nice metal stands. I bought them from a friend.

Wire = Nothing. I already had them in storage.

The receiver was in near-mint condition. The sound was really ... really good. If I had to do it over today, I wouldn’t have bought the Radio Shack CD player. While a good player, one can do better today shopping eBay for a good, used higher-end DVD player.

So, I made $200.00 on the speaker trade, so that has to be deducted from the total cost. That brings the overall cost of this little killer bedroom system to $365.00.

Frank

Well, good no but not too bad maybe.
Used original Audiolab integrated - $250.
Some used DVD or CD player - $150.
This leaves $350 for used older speakers and cables.
Yeah, there will be some sound coming out.

Of course!  If you only spend money where it matters. 
Streamer - very marginal gains, if any at all, over a Raspberry Pi 4 plus Allo HAT.  $100. 
DAC - Khadas Tone Board. Excellent. $100. 
Any class D low distortion amp. $300. 
Van Damme cables at $4 per meter. 
Mark Audio Alpair 11MS full range drivers. $150. 
$100 left for some birch ply. 
Then get the free plans for the Frugalhorns Mk3 : https://www.frugal-horn.com

Bingo! 

Another option is to spend $700 on the best active speakers you can find, $50 on an Audioquest JitterBug, and hook them up to your laptop.

That’s a great suggestion. Although not full range could add a cheaper sub later.