I also "started" watching anime on tv remi, saint seiya, dragon ball, sailor moon, candy candy etc but for me that wasnt anime, those were cartoons. What really got me into anime was Evangelion, on VHS, japanese dub, with english subtitles (english is not my first language and I was way worse at it back then than I am now) A sacred piece of imported media lent to me by my old sister's friend.
My mind was blown, I have never seen something like that. Of course I had seen mechas before in voltron and macross but never something this complex, detailed, emotional, and full of meaning (and with nudes!!!). It was like watching something awesome and forbiden for young me. I watched it in less than a week, I understood less than half of it and I loved it.
The next anime he lent me was SE Lain. This one I still dont understand it.
Now that I think about it... I think he wanted me to get brain damage.