Before you buy anything
A few things worth knowing first
The turntable is only part of the system. You also need a phono preamp (to amplify the cartridge's tiny signal to line level) and speakers. Some turntables have the preamp built in — those plug directly into powered speakers or a stereo receiver. Some don't — those need an external preamp. Knowing which you have before buying speakers saves a frustrating afternoon of troubleshooting silence.
Don't buy a suitcase or all-in-one record player from a big-box store. The Crosley Cruiser, Jensen JTA-230, Boytone BT-101TB — all of them. They look like a good deal at $40-80. They're not. The needles are cheap, the tracking force is wrong, and they will physically damage your records over time. The price difference between a Crosley and an AT-LP60X is $30-60. It's the most important $40 you'll spend in this hobby.
Used records are usually fine. Most LPs in circulation were pressed in the 1970s and 1980s — well-made, heavy vinyl that lasts forever if stored vertically and kept away from heat. A used record in VG+ condition from Discogs for $5-15 sounds as good as or better than a new $30 pressing. Start used, build a real library, then graduate to new pressings once your setup is ready to reveal the difference.