Hi Jeff,
Re-issue mono records will play on stereo just fine, although a true mono cartridge still sounds quieter. KAB makes a mono switch that is not expensive that would do the job too.
As for a place to start: Time-Life offered a series on vinyl entitled the Giants of Jazz. There were 28 volumes in the series, each volume comprised of 3 records and included an excellent booklet written by a recognized music scholar. Each volume featured one artist, and of course each artist was accompanied by important sidemen of the day. This series is a great place to start because it was widely distributed and copies are easy to find and usually very reasonably priced. The quality is audiophile grade too. Look at Amazon and Ebay to begin your search. This series will take you from the early roots of jazz up to the beginnings of Bebop.
Bebop and an off spring of it usually known as Cool Jazz or West Coast Jazz started about the middle of WWII and lasted well into the 1960s. After that came Fusion or Jazz-Rock, which I am sure you can intuit on you own. If you want to skip ahead just to get the flavor of this stuff, for Bebop pick up an Dizzy Gillespie/Charlie Parker record, or pick up a Johnny Costa CD. Johnny was the pianist for the Mr. Rogers show and he played Bebop that sounded so much like Art Tatum that even Art Tatum himself was fooled. Not many people know this, btw, but Charlie Parker was playing Art Tatum riffs. For the West Coast sound, either Dave Brubeck Quartet - Take Five, or one of the Peanuts cartoon character records like Charlie Brown's Christmas, the music was all written by Vince Guaraldi and is West Coast jazz to admire. For Jazz-Rock, start with the man who invented it Miles Davis and get Bitches Brew. Follow that up with Weather Report's Heavy Weather.
But get grounded with early jazz first then get back to me. At any time, if you need a break from your jazz lessons listen to some Bob Dylan, who just might be the best blues lyricist ever. There are many great black singers. Someone might tell you that Robert Johnson was the best blues entertainer ever. Forget that. Besse Smith was the best ever, male or female. This might seem unrelated, but once you get yourself saturated in the roots of jazz you will find that it all comes from the blues. So, don't get all uppity about what kind of music should be labeled jazz. Duke Ellington didn't even like the word jazz. His autobiography was entitled "Music Is My Mistress."
You are in for a great adventure.
Bill