Find which instrument you prefer (sax, bass, piano, trumpet) then choose from John Coltrane (sax), Charles Mingus (bass), Thelonious Monk (piano) or Miles Davis (trumpet). Those are four good starting points.
As someone who didn't know jazz from a hole in the head a few years ago, I would try these albums specifically, to start:
Coltrane - A Love Supreme (it really is a good album and lives up to the hype)
Mingus - Mingus Ah Um
Thelonious Monk - Monk's Music
Miles Davis - Kind of blue (for early period) or Bitches Brew (mid period)
The reason why Miles gets two is because he had a long-spanning career. I would also avoid late period Coltrane initially as that might be too "out there". I still have a hard time with his late period stuff, but ALS seems to blend the two periods well.
I personally like Dexter Gordon a lot, but I'm not sure if he's a good place to start. But I would still recommend "Go" as a starting point for him, if you want to try a sax player other than Coltrane.
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