I got some of my friends interested by lending them some manga, but I weighed out in my mind what kind I should give them that they'd like. I don't think there is just one you could give to anyone (anime or manga) and they would all become interested. One friend I got hooked on by lending her the series Rayearth to read, then I got her started on Vampire Game. She proceeded to buy every volume available after that .^_^. Whenever I buy gifts, I usually get the first volume of Vampire Game .^_^. Another one of my friends I lent Planet Ladder, and like I said, then bought her as well the first volume of Vampire Game .^_^. They tend to like it, but as I mentioned, everyone might not be inclined to be interested in it.
As for an anime, I want my friends to watch R.O.D the OVA, it's not too long and it's interesting .^_^. Just off the top of my head though
Anyway, I'd stick with Hayao Miyazaki movies to continue to get her into anime. They are hands down, without a doubt, classics.
What got me started? *laughs* I don't remember.... .^_^.