It has been entirely too many moons ago, since I first started watching Anime, to be able to remember what my first was.
This was back around 1987, before most of us had internet, when I was renting movies at Blockbuster and almost all anime was still massive destruction, lots of explosions, tons of TnA, and none of the stereotypical story lines that almost EVERY show has in it now.
Some of them that I remember renting tho. The old Original Fist of the North Star. Geist/Most Dangerous Geist, Devilman, Tank Police, Guyver, etc. I think my all time fave is kind of a toss up between Guyver, and Bastard! Tho that one is kinda cheesy now a days.