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!