Where possible, I try to get Japanese-only versions of these movies and show them while reading a script aloud. Friends of mine who know Japanese find this distracting, but most folks who come to my showings agree that it's the best way to see a Japanese film! After a few minutes, you tune out the voice of the reader, and you get the sense that you're actually understanding Japanese somehow. And this frees your eyes to enjoy the amazing animation and background art, while also enjoying the wonderful and talented Japanese voice actors.
When I can't get a Japanese-only copy and script, then I will show a subtitled version, if possible. I get my subs from friends of mine who are connected in the anime fandom community here in America. Fan-subs, made for the love of it, are often more true to the original. They also often have culture notes here and there to help American fans understand the more subtle aspects of Japanese culture and puns. [Note: now that many anime are available commercially, I do my best to support the American anime industry and buy commercial releases -- even if I don't like the dub or sub.]
When I can't get a fan-sub or a commercial sub, then I will resort to a dub. America is not set up do make dubs like many other countries dubbing from English into their native language, so often English dubs are not very good quality. Notible exceptions are Totoro and Princess Mononoke, but such quality is hard to find.
Here's my descriptions page.
Here's some links to script sites:
Anime and Manga scripts from Animaga Services
Central Anime -- timed scripts for subtitling machines [I wanna get one someday!]
fansub.net -- BIG source of scripts!!
Anotated Mononoke Hime script -- not looked closely at this, but pretty cool
that the Japanese is in romanji! Helpful to those learning Japanese!
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