You can't go wrong with Ghibli movies.
As for series, it depends on the person. When I suggest stuff to my teachers or anyone say, over 30 or something. I dould recommend Monster, Baccano!, Gungrave.
For the younger audience like my friends 16-20 for some reason they liked shoujo comedy stuff, Lovely Complex, Kimi no Todoke, Ouran Highschool. Not saying they're bad by any means

Of course there's always Bleach, Naruto, One piece. Most people around me watch those and hardly know anything about anime.