I think, for a lot of us, the pre-Crisis years of the New Teen Titans are better than the post-Crisis years. So, it's 1985, what direction do you take the characters, and what story arcs are you going for? You can start either with issue #12 (last issue before Crisis tie-ins) or issue #15 (first issue after).

Right now (please correct me if I get these wrong):
Trigon is dead, and Raven has disappeared
Titans are well-regarded after Trigon's defeat
Lilith is on Olympus
Sarah Simms has a new boyfriend
Steve Dayton is dying (if pre-Crisis) or has used helmet and is mad (post-Crisis)
Kole is either just joined or just killed, depending on pre or post Crisis
Starfire has agreed to go back to her homeworld (if post-Crisis)