New TT or old

I see nothing wrong with playing your LP's on a turntable of the same vintage as your vinyl. Do it, and enjoy it. If you decide to get more into it later, I'd recommend a record cleaning machine before upgrading the turntable. Just my two cents.

I faced a similar situation several years back, when I had my old B&O turntable. I recommend selling the B&O TT on Ebay for whatever you can, and then moving on up into something easy to use, like a Rega P3 or something similar. (Don't forget that if you are getting back into vinyl, that you'll need a decent phono preamp, as well as all the cleaning supplies.)

IMHO, The B&O turntables were fine at what they were, which was a top of the line, mid-fi table. (The best thing about them was their cartridges were well enough made and had a light enough VTF, that all of my old records sounded great when I upgraded to a Basis 1400.

Good Luck!

A record cleaning machine would make the most positive impact at this point.

Sell the B&O and scrape all the money together you can. Then buy a new (secondhand) recordplayer and cartridge, and spend some money, as Dean suggests, on a record cleaner.