If we're going to go into the new wave, you'd better set some solid background to the movement. Bresson (Pickpocket, A Man Escaped), Renoir (Rules of the Game, Grand Illusion), Dreyer (Passion of Joan of Arc), Cocteau
Godard isn't for everyone--in fact, it's not for most people. It's very esoteric and requires a vast knowledge of film, philosophy, and politics to really digest. But, hey, even though I lack alot of those qualities I find myself loving him. Band of Outsiders and My Life to Live are my personal favorites.
Truffaut I love, absolutely love. Even his later stuff like Small Change really gets me. He has so much more warmth and heart than Godard, and his relatively conservative nature in the new wave helped to keep the movement grounded in practicality. Oh, and The More You Know: Truffaut wrote Breathless. Found that out the other day.
Ingmar Bergman is an unbelievable artist. Cries and Whispers is the most devastating experience put to celluloid, and it's no contest. Another whalloper is Tarkovsky, especially Solaris.
Don't forget to check out american greats like Wilder, Altman, Ford, Woody, Scorsese, and Malick (yeah, I said it).