Upgrade CD player or get into LPs? Suggestions

Do it all.
I would buy a budget turntable to dip into vinyl. Vinyl is a new paradigm for you, and there are software issues (you may not be able to find playable lps of the music that you want to listen to). An entry level Rega or Pro-Jett, or Thorens table can be had for a few hundred, and remember to budget for a phono pre amp. If you get into vinyl then upgrade in the future.
With the remaining funds I would by a CDP with good digital inputs so that you can branch into computer audio. Basically you would look for a good DAC that also spins CDs.

Lately, every lp I had gotten seemed unplayable to me, filled with noise. This applied to internet sales where the buyer listed the product as nm and to lps that
I purchased in stores that looked great on inspection.
I think the problem was deterioration in the stylus. Genius that I am, I hit on this when the stylus was hanging almost at a 90 degree angle to the cartridge body.
I used this as an opportunity to do a long deferred upgrade to the whole vinyl rig. Specifically I went from a Rega P%5 with with it's stock mm cartridge to a Clearaudio Concept with the Concept mc cartridge. Now, all those recently purchased lps that sounded so damaged sound playable.
Lesson: 1) I ain't to swift, and
2) make sure your stylus is in good shape if you think that the noise level from your vinyl is unacceptable.