Well, to be fair, it would have to be Pokemon/Dragonball/Digimon. But the one anime that got me actively looking into anime (which is what I would consider a first, Pokemon/Dragonball/Digimon is a standard), would be Love Hina.
I think the first true anime I watched even though I didn't fully understand it at the time was Blue Submarine 06 when it was on Toonami, but what really got me into anime was probably Gundam Wing.
I watched the standard pokemon/digimon/dbz for my first anime too, but the first anime that I went out and looked for was Renkin 3-kyū Magical? Pokān after seeing a cute picture from it.
It's a bit blurry, but I think Dragonball Z. Pokemon maybe. Ruroni Kenshin was the first series I really invested myself into, and Neon Genesis Evangelion was the first series I ever downloaded. I was not old enough for that shit and it was wonderful. God bless Toonami.