Jazz music recommended

Charlie Parker and John Coltrane and Ornette Coleman are obvious choices if you like sax

This has been covered many times before, but I'll bite.

What Jaybo said plus John Coltrane, Sonny Rollins, Kenny Burrell, Ben Webster, Charles Mingus, Roland Kirk.

Basically look at the Miles Davis Quintets from the late 50s into early 60s, and follow all their members careers. It's the family tree! (An oversimplification, I know )Cheers,
Spencer

Thelonious Monk, Albert Ayler, Charlie Parker, John Coltrane, Sun Ra, Ornette Coleman, Don Cherry, Jackie Mclean, Eric Dolphy, Charles Mingus, Cecil Taylor, Pharoah Sanders, Lester Young, Archie Shepp, Mal Waldron, Marion Brown, McCoy Tyner, Louis Armstrong (duh), MIles Davis, Art Ensemble of Chicago, Charles Tolliver, Randy Weston, Sonny Sharrock, Anthony Braxton, Bill Dixon....how many more might you want? I might have to go look at my collection!

Sbank is right! You listen to a few cats here and there. This guy played with that guy whose also on so-and-so's album. Next thing you know, you have yourself a library. However, if you're looking for "the more simple format", I don't think Mingus is what you want.
Buy a few Ray Brown albums, Bill Evans (Waltz for Debbie), Chet Baker (Chet), Wes Montgomery, Stan Getz. Of course, no jazz collection is complete without Kind of Blue. Just don't go too late into Miles's carreer-stay away from the fusion stuff (Bitches Brew). That was my first jazz album ever and I hated it. I decided to give Miles another chance. My next album was Kind of Blue, and the rest as they say....

Kieth Jarrett, Tomasz Stanko, Bobo Stenson, Gene Ammons, Dave Holland, Herbie Hancock, Chet Baker, Tommy Flannagan... This might be a very long thread.