Start with Akira, then Neo-Tokyo, Ghost in a Shell (1995) then Ninja Scroll, Fist of the North Star (1986), Crying Freeman, Berserk (1997), Devilman (1987) <-- hard to find, Appleseed, Princess Mononoke, Castle of Cagliostro: Lupin III, Wicked City, im noting movies with great animation and great stories. If you can make it through those movies, any dragged out anime series you can get into.