When I moved for the first time, we had different TV channels (1999 cable TV) and saw Pokemon for the first time. The movies got me more interested, then I got into Dragonball Z and I didn't get past that stage for a few years, that show was the szchit for the 90s kids my age back in middle school.
After watching a few of the Miyazaki movies and watching toonami for a few years, my gf told me I should check out a show called Bleach. This was in 2006, and I fell in love it after seeing some of the later episodes on adult swim months later in a log cabin up in Big Bear. After that, I went home and binge watched the show, close to 10 episodes a day by the time summer hit and damn was it hot, no AC so it was about 95 degrees in my room for most of the day, but I didn't care! The show was amazing! Especially when comparing it to american television. I only liked a few american tv shows, and I still get really picky about what I watch. Anime is only limited by the artist's style and tools, the story and script, while live action tv shows need a lot more funding to be good quality, so often the special effects are terrible and the acting is cheesy. As much as I got into anime, I never wanted to go to an anime convention.
Anyways Bleach got me really into anime. I think the best anime I've seen were so good, I can't stomach the low quality stuff that plagues the industry, so the list of acceptable series has really thinned out.