Have a look at a Peachtree Audio Nova 150. You should be able to pick one up used within your budget. I drove my LS50s with one for several years, before I upgraded to separates (Purifi based amp, paired with a Schiit tube preamp).
Best Integrated Amp (for me)
I recently upgraded to a Pro-Ject Classic turntable. I currently own KEF LS50 bookshelf speakers and a Nikko NR-719 tuner (from the 1980s).
I'm interested in upgrading to a better-quality (and nicer-looking) integrated amplifier to pair with my turntable and speakers. I love things that are really simple and classic-looking (but of course I also want it to sound great). I'm looking to spend somewhere between $500-$1000.
Any suggestions would be most appreciated!