I unfortunately don't remember the first jazz recording that I bought. It might have been the Red, Hot, + Cool Stolen Moments CD back from 1994. I didn't buy it for the jazz tracks on it though...I also got Jazzmatazz back then but that was for the MC Solaar track.
I've put the story of the first dedicated jazz records I got below as a gift. I'm not sure it entirely goes with the spirit of the original question so feel free to disregard.*
10. “Foxy Lady” from Jimi Hendrix Experience Greatest Hits. I was in sixth grade when I heard this shit in Wayne’s World and knew it was dope. My friends said I was gay for buying an old record at the mall. I think one of them bought Boyz 2 Men.
*11(?). Kind of Blue, Smokin' at the Half Note, Hear No Evil, Bitches' Brew, Head Hunters, and a few others.
My best buddy is an amazing jazz drummer and he'd been giving me a hard time for a long time about not owning a record player. He finally just up and gave me a nice B&O turntable and a bunch of records for my birthday. I plugged it into my main system and let it collect dust until one night I was bored and said to myself "OK, I'm going to give this an honest go and see what the fuss about jazz is." Here I am, three turntables and >500 records later, lol.