I find it a hard call to make. Mostly due to separating the older from the new characters at the time and well, just liking them all.
I guess for the older characters it's Robin/Nightwing. For the "new" characters it was really Cyborg. Starfire came close to her being a bit naive and powerful, but really it was Cyborg for dealing with all he had to deal with.
Not much has changed so not much has changed in my views on the characters except perhaps with Starfire and Raven. Starfire is as known, become a bit of a tart and I don't like that. I prefer the classic version of the animated one. As for Raven, I became more of a fan of the animated version then the classic.
I was barely a fan of Jericho, did not care for Terra as she was a double agent from day one. After 1984, I was no longer reading NTT so the later characters had no real affect on me as I didn't really know them.
I do think however, Changeling was something to note. He was perhaps of all the older characters, the one most changed. Kid Flash's grumpiness was new, but okay. He was like Quicksilver lite. But with Gar... he was something new while being something old at the same time.
"Why are you pointing your screwdrivers like that? They're scientific instruments, not water pistols."
"Oh, the pointing again! They're screwdrivers! What are you going to do? Assemble a cabinet at them?"
"Are you capable of speaking without flapping your hands about?"
""Timey" what? "Timey wimey"?"