Going along the same path, I watched Sailor Moon and Pokemon but just thought they were regular English cartoons since they were mixed in with such. The first anime that I watched that didn't air on a cartoon channel was actually a movie: End of Evangelion. Found it on the internet when I was around 10, watched it, didn't understand it, saw Asuka's scene, and got emotionally scarred for the rest of my life.
If we repress EoE like I've been trying to for the past 10 years, then my actual first anime was Alien Nine. I read the manga and watched it at my cousin's house when I was maybe 11 or 12 and then completely forgot about it (and anime in general) until about two or three years ago when I realized that I have a lot of free time that doesn't overlap with the free time of my friends. One day in 2010 I stayed up until about 4 in the morning when I found a clip of episode 6 of Deadman Wonderland on Youtube and I thought it was the most awesome thing I've ever seen so I marathoned it and decided to watch more anime.
Then I fell asleep and the next two years were all one big dream, during which I watched way more anime than I should have.