As someone who listened to classical before discovering jazz, I've brought with me a preference for jazz that emphasizes composition. I like improv, but for my taste too much jazz glorifies the improv solo at the expense of the overall composition and structure of the song, and the results are often a bore of tag-team soloing. (I'm not a bop fan.) I prefer it when the solos are woven into the structure of the piece. I also want my jazz to swing and be fun. The mind working with the head bobbing. With that in mind, I would recommend the following:
Louis Armstong, who to me epitomizes the heart and soul of jazz
Benny Goodman, I particularly like his small trio and sextets. There's a lot more big band that is underestimated as good jazz.
Gerry Mulligan Quartet
Dave Brubeck
Count Basie
Duke Ellington
Miles Davis
Horace Silver
Oscar Peterson
Bill Evan also would fit here, but he's not my cup of tea for other reasons.
And a very different kettle of fish, but Pat Matheny. I can't stomach all of his work, but at his best he can craft a terrific composition
Vocals also tend to ground jazz into some overall stucture, though some jazz vocals can be too light on the jazz.
If anyone else has suggestions along these lines that I haven't mentioned please pass them on.