I'm a bit late listening and thus responding, but figured I'd give my "story". I have two, sort of.
First, I have a show I was really into as a child that I later recognized was anime: The Mysterious Cities of Gold. It has a hilariously awful 80's dub(although I love it), but the story is really fun, and actually has a lot of PoC as main and secondary characters. Also, a super-catchy main song.
But, I first got into anime fandom when I was in 10th grade in about '96-'97 when a classmate brought in her Ranma 1/2 manga to Latin class and I started reading it. So I read more and watched the anime and fell in with the little clique of anime nerds at school and was really into it all through my first years of college, before it became more of a side interest to general western sci-fi/fantasy fandoms. But, along with Ranma was Fushigi Yuugi and Escaflowne and Eva and Marmalade Boy and Child's Toy and CLAMP and Gundam Wing and Serial Experiments Lain in HS. Later it was FMA and Hikaru no Go and Fruit's Basket and Cowboy Bebop and Trigun and so much more.
And, while I've never really quit it, I've been getting back into anime recently due to Yuri on Ice, and I'm really appreciating the massive amounts of fanfic that have grown up around it! I'm seeing more of overlap of western fannish conventions(labeling, etc.) in Yuri on Ice than I remember for other anime, but that might be because I read most of my YoI fic on AO3. (And, I have looked for fic yet, but I loved the first season of March Comes in Like a Lion; it's so contemplative.)