Jazz composer is an oxymoron. Composer to me means sculpting every detail.Jazz means improvisation.There are jazz standards that are being written but this is just a skeleton for improvisation existing out of a melody and a chord progression, nothing more.
As for jazz musicians. I prefer Charlie Parker and John Coltrane. There are many more great musicians. Art Tatum seems to appeal to many pianists here. There are guitarists like Pat Metheny, Jim Hall and Pat Martino. More modern jazz pianists like Chick Corea and Herbie Hancock, both of them play electronic or rock jazz too. But generally I think you should move away from piano if you are going to submerge yourself into jazz. The superior instrument in jazz is the saxophone by far. Check Sunny Rollins, Micheal Brecker, Cannonball Adderley, Dexter Gordon.Maybe the easiest way to get into jazz is through pianists. The best most jazz-like pianists are probably Thelonious Monk and Bud Powell.
As for jazz musicians. I prefer Charlie Parker and John Coltrane. There are many more great musicians. Art Tatum seems to appeal to many pianists here. There are guitarists like Pat Metheny, Jim Hall and Pat Martino. More modern jazz pianists like Chick Corea and Herbie Hancock, both of them play electronic or rock jazz too. But generally I think you should move away from piano if you are going to submerge yourself into jazz. The superior instrument in jazz is the saxophone by far. Check Sunny Rollins, Micheal Brecker, Cannonball Adderley, Dexter Gordon.
Didn't Waller take lessons from Godowsky?