It's not hard to find a decent vintage direct drive Yamaha or Pioneer PL series for $300. You probably won't find a PL530 for that price, but you can get a PL510 in great condition and it will absolutely trounce the entry-level Pro-Jects and U turn.
Find a nice vintage Pioneer, pair it with a Shure M97xe or AT120eb cartridge and you'll get very respectable sound for your budget.
Find a nice vintage Pioneer, pair it with a Shure M97xe or AT120eb cartridge and you'll get very respectable sound for your budget.