Hmm, this is a toughy. I can definitely say which anime first got me steadily into the genre, but not which I watched first.
When I was little, I used to watch shows like Voltron, Battle of the Planets, Macross, Transformers, Speed Racer, and the like. There were a couple other space ones, but I can't remember their names. I caught a couple Sailor Moons, but I kept forgetting when it was on.
Later, I found more Sailor Moon (which I loved) and the Sci-Fi channel used to show anime movies really late on Saturday nights. There I saw things like: Iria, Zeiram the Animation, E.Y.E.S. of Mars, Armitage, all of which are special favorites to me.
Tim and I had a friend in college who was into anime. She showed us Project A-ko and Bubblegum Crisis. Two awesome shows. She also broadened my love for Sailor Moon (she was a Moonie, too
). We tried to rent anime here and there from the local video rental, but the selection was extremely limited. One series we rented years ago was The Guyver, Bio Booster Armor, which just came out in a dvd box set. I surprised Tim with it which thrilled him to no end.
lol
Then Sailor Moon came out on Cartoon Network and the rest is history.
That show got me steadily into anime and now I can't get enough.
I think the Toonami block then was Thundercats, Sailor Moon, Dragon Ball Z (the beginning when Vegeta was bad), and Johnny Quest. I believe Ronin Warriors and Gundam Wing were the next shows to join Toonami. Tenchi was shown not much later.
My first manga was Sailor Moon, followed by Gundam Wing. Then I got Dragon Ball and No Need for Tenchi.