My intro was likely Voltron, though I had no idea it was "anime" due to how young I was (preschool age).
The actual anime that I knew was anime (even if it technically isn't), that got me started on the long road towards devouring hundreds of series since, was Robotech.
It gets way too much bad rap from western anime fans, many who pretend it was the worst thing ever, but as someone who lived (and loved) it when it came out, I liken it to how when FF 7 came out JRPG fans were in love, but now many won't dare admit that they enjoyed that game.
Listening to youngsters these days ape old arguments concerning Robotech, while pretending they were even on their parent's radar of conception at the time it came out, is always amusing.