My strategy for building a jazz collection is what I like to call the "pub crawl" method. Focus on a single recording or set of recordings, one you like but preferably one that is also recognized to be fundamental to the history of the music, and then use that as a point of orientation. I began with the four recordings by the Miles Davis Quintet in 1956: Workin', Cookin', Relaxin', and Steamin'. Each one is brilliant, and together they give you a good foothold in the most important period of jazz.
Where do you go from there? Well, the Miles Davis Quintet later became a sextet, with the addition of Cannonball Adderley. You could look into that. Then there is the second great quintet in the sixties, with Wayne Shorter replacing Coltrane, and Herbie Hancock on piano. Another avenue along with to crawl is to follow the work of the various members of the original quintet in the same period. Coltrane does a lot of brilliant work on his own, and the rhythm section consisting of Red Garland on piano, Paul Chambers on bass, and Philly Joe Jones on drums, produces its own body of work. Then do the same with the sextet and the second quintet.
The reason for crawling rather than jumping about is that it allows you to build a coherent map of the music, and thus you can intelligently compare different recordings. It will also allow you to identify periods in each artist's career that you want to avoid. During the late sixties and seventies, a lot of brilliant jazz men recorded some atrocious stuff, as most will readily admit. But that doesn't mean you can't pick more than one artist or combo to use as points of orientation. As you feel your way along, you will find a number of great recordings, jazz geniuses, and spectacular groups to collect and explore.
Jazz is one of America's great contributions to world culture. Even the French like it! Today it is available to almost anyone who takes an interest in what is brilliant and beautiful.