It's key to not try to introduce someone to anime with a series that is too Japanese. Anime makes a lot of cultural assumptions of its audience, and viewers can be put off by a lot of things they don't understand because the authors and production companies just assume the viewers know or would never be bothered by it because it is considered normal.

Its often better to start with something that plays to the particular strengths of animation in general. Fantasy or scifi being the most obvious, where the special effects never look like out of place mismatched CGI that live-action has to deal with. Usually series with a more western feel are even better because they don't use those same Japanese cultural mainstays. To the more western cultures, anime has an advantage of slightly more mature storylines than typical animated series of the west.