First investment into a turntable

Here ya go!
https://uturnaudio.com/pages/turntables

Not to rain on your parade, but your old albums are likely chewed up from whatever they were played on in the past and $2-300 does not exactly equate with "beautiful sound" even from an entry level standpoint. Turntables involve a lot of moving parts and vibration issues that take a bit of money to address.   That said, the Pioneer 500 doesn’t look too bad for $350.  
Just try to be realistic.
https://www.amazon.com/Pioneer-DJ-PLX-500-K-Direct-Turntable/dp/B01K1WUS9O/ref=sr_1_2?ie=UTF8&qi...

Some of the old early 80’s HK turntables can be a great deal.

Some things usually need to be done, though. In the HK tables they may need new damping foam in the sprung footers, but that is an easy job.

A notable problem is finding good arm bearings in older tables, at that price range.

also look into mico seiki turntables. Some of the most notable ’brand name’ Japanese turntables were made for those brands by........ micro seiki.

Go to hifishark and type in ’micro seiki’ or Harmon Kardon tc (tc-60, tc-35, tc-65, etc)

Your most important thing to learn is setting up the cartridge on the arm with the correct geometry/alignment/position. This will have the biggest effect on your overall fidelity of output.

I mean..heck..right here on the ’gon..:

https://www.audiogon.com/listings/turntables-restored-2018-01-10-analog-befcdf57-a6a0-4bae-8c46-8716...

I’m not saying it is the best buy, but they show up everywhere. So go fishing and you can spend some fun time learning which is the best micro seiki, and some of them are quite gorgeous. Completely manual tables are always the best sounding. you can add a manual arm lifter thingie as a aftermarket ad on.

Getting auto lift is generally bad news as it adds a bunch of mechanical garbage to the arm and thus interferes with the mechanics of vibration in the arm and thus makes records sound worse. all for convenience. the strippers (fully manual tonearm operation) are always the best sounding. Note that nearly 100% (~+99.9%) of all ’real turntables’ have purely manual tonearms. $100k turntable? fully manual? Not a chance it would be any other way.

200 -300 is a tough range. Older pl pioneer series are going for double that price. Same with vintage denon. Most of those are bullit proof. Look for a vintage Yamaha as you can find a decent direct drive for around 300-400 and they are very well built as well as very nice looking. Good luck and happy hunting. 

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.