To touch on movies a bit more, I would definitely recommend 5 Centimeters Per Second, and anything from Studio Ghibli. I'd probably start out with Spirited Away, since a lot of people have seen and love that movie whether the enjoy anime or not(I know a lot of people who don't watch anime, but told me they grew up on that movie). I feel like The Secret World of Arrietty would be a good one to start out with as well!
As far as series go, depending on the person, I would tell them to watch Gurren Lagann or Attack on Titan, since they were both pretty popular across the board. Over rated or not, how would this kind of person know, right? ;)
Slice of Life anime might seem too dull to someone just starting out, so I would bring up a slice of life comedy I actually really enjoyed(which is rare, I always get bored with SoL), Gekkan Shoujo Nozaki-kun. I feel like that show is just realistic enough to hold someones attention, as well as make them laugh cause oh my god was that show hilarious. The Melancholy of Haruhi Suzumiya is also a really good one.
I've always felt like the more popular anime are always better to start out with, rather than the oblong ones that were barely talked about in the English speaking world. After all, they got popular for a reason, right? That, and shorter series are a plus for newbies. Like Cherrim said, it makes for less of a commitment.
