I started out with Dragonball Z and Rurouni Kenshin, but was before I even knew what anime specifically was. Once Naruto started airing on Toonami, I watched it knowing what it was and where it came from and everything, so you might call it my first. The anime I first watched that didn't air on American television was probably Toradora, but I can't make that call for sure.
First manga was Naruto, a long time ago. I started reading it in the middle of filler episodes since it was ahead of the bullshit. Liked it a lot better than the anime, too. First manga I completed (and marathoned through) was BECK by Harold Sakuishi. Still my favorite manga to date.