Exactly my first anime was the king of shamans, and then the Naruto culture began, in general, in my country they are still very skeptical of anime as a genre, but I still managed to legally watch it as a child!
I started with Naruto, Pokémon, Dragon Ball Z, Zatch Bell, Tokyo Mew Mew and etc on TV, but at the time I had no idea what anime was. I think the first one I watched, once I knew what it was, was Death Note.
I watched a bit of Toonami when I was younger, but I'd say my first actual anime was Angel Beats!, which was maybe not the most emotionally-wise one to start with. :(
My first was Candy Candy! :D
I remember my mum was a fan of the original TV run and played it for me as a child, it grew on me and I've loved animes ever since!
Inuyasha, they used to show it on broadcast tv so my mom used to put it on for me and my sister. I think they where other series, but I don't remember which ones.