I recently went down the same rabbit hole - enjoy! You can’t go wrong going straight to the main series. Or - If you want to do like me - I did a serious deep dive of related comics before starting the main series… Justice Society Returns miniseries, all of Stars and Stripe, the 3-issue Doctor Mid-Nite miniseries, Spectre 54 (Mr. Terrific intro), JLA 27-31 (gathers the JSA back together and introduces JJ Thunderbolt), Power of Shazam 45-47 (sets up Black Adam who is a major player in JSA), the Hourman series… hmmm am I forgetting anything? You could read Wonder Woman 125-136 which explains why Hippolyta is back to being a superhero.
Before you start the main series, read JSA Secret Files #1 which sets up the plots. As you go, there’s also some tie-in issues that are pretty relevant. Here’s the issue listing from the JSA by Geoff Johns TPBs:
JSA SECRET FILES #1, JSA #1-25, JSA: Our Worlds at War #1, JLA/JSA Secret Files & Origins #1, JLA/JSA: Virtue and Vice, JSA: All Stars #1-8, JSA Annual #1, JSA Secret Files and Origins #2, JSA #26-81
Lastly, right around JSA 25 or so, you should read the last issue of Starman #80, for a major event in Stargirl’s life