Hi,
I'm new here and just saw your post on the home page.
I have literally a few thousand hours of anime and a few hundred pounds of manga around my apartment.
The best anime ever is Neon Genesis: Evangelion, which can be slow moving and very thinky at times, but is still the best.
There are two Ghost in the Shell movies, and two TV series. Any come highly recommended.
For mindless fun, I enjoyed all the assorted Tenchi Muyo, El-Hazard, and Slayers series.
If you like action, Trigun is a silly comedy that slowly turns into a serious drama, and Cowboy Bebop is a semi-serious drama that turns very serious.
Kamichu is sweet, harmless innocent fun.
If you have high-speed internet, go to www.animesuki.com for torrents of legally downloadable, fan subtitled anime that is not currently available in the stores.
Hope that helps.