I watched pokémon and dragonball z when I was young, but my first real anime was either
Madoka Magica:
or Shugo Chara:
Which has been probably more than 6 years ago since I watched that, it's so old it wasn't even on my anime list saying that I completed it.
My friend who really loved anime introduced me with "easy to watch" animes like these. And ever since I've been part of the culture.