Definitely watch Ghost in the Shell, the first movie. Every other GitS is between mediocre and horrible (on my rating scale, at least), so don't bother.
I would also recommend
Whisper of the Heart, a modern fairy tale in suburban Tokyo. Beautiful, beautiful movie, although somewhat simple.
Now and Then, Here and There is a must-see. Also a fairy-tale (notice a pattern here?), but a lot darker, and very touching. Also, its art directing is my favourite amongst all animated series I've seen so far.
Finally, Cowboy Bebop. Simply the best soundtrack, like, ever. Jazz and cool bounty hunters? Hell yeah.
