Anime movies

So i'm a big fan of films of pretty much any kind and i'm quite well versed in a lot of styles. I also love animation but i have to admit that i know pretty much nothing about anime movies.

I did watch Dragonball Z and Pokemon as a child and i did see one anime childrens film a year or two ago that i thought was excellent as both a kids film and a film in general.

So anyone have any suggestions for things that i could view to get a taste anime?
No TV series please unless they are very short thank you :D

Oh! P.S. Make them things that it might be likely for my library to have, so nothing too obscure ;)