Fist of the North Star is mandatory viewing. Please watch the TV series before the movie though, or for that matter the OAVs that just recently came out... I'd also like to take this opportunity to recommend Kimagure Orange Road and second Maison Ikkoku (these are powerfully 80s) and then some more modern romantic comedy. Then go for Aura Battler Dunbine and Escaflowne. This'll provide some interesting historical perspective. Most Miyazaki movies are class; my personal favorites are Lupin III: Castle of Caglisotro, Porco Rosso and Laputa (aka Castle in the Sky). I also like anything by Yoshitoshi Abe; I'd start with Niea_7 since that's relatively light fare.
