To touch briefly on this debate, I agree with Goji and have always stood by this: cartoons are animation regardless of country of origin. In fact I often choose to avoid saying 'anime' altogether in place of 'Japanese animation' to avoid splitting hairs.
For users like WinterMillennium I will say it's tricky to recommend one particular place to start with Japanese animation; however I personally would certainly dip into the popular side of the spectrum first with films like Akira, Ghost in the Shell and Nausicca depending on your personal taste.
I will say I did just see Ben Wheatley's latest film
Sightseers the other night, bloody good it was.
