Read these comics in this order:
Booster Gold v1
Blue Beetle v1
Mister Miracle v1(Ted and Michael show up often here) (All three of these run almost concurrently with JLI)
Justice League International v1(issues 1-25) -> Justice League America(issues 26-91)
Extreme Justice (starts around JLA 91, also beware of 90s)
They hit limbo around the end of Extreme Justice, and both will show up sporadically and separately throughout various comics. Ted often guest stars in Birds of Prey, and Booster will sometimes show up in JLA or Superman.
Start back here:
Formerly Known as the Justice League
Superbuddies (aka JLA: Classified 4-9)