Not sure if everyone would consider it “anime” as it’s more a hybrid of US and Japanese, but “Flight of Dragons.” It felt very stylistic and deep to a young me, and showed me animation could be serious.
As to specifically watching anime as a known thing, Toonami shows pulled me in. I caught DBZ flipping through the channels and I started watching that and Outlaw Star.
Met a friend that was into it and he lent me Iria: The Zeiram, Armitage 3, Ghost in the Shell, Vampire Hunter D, and eventually a few others.