If she likes crude humor, consider Shin-Chan.
I've watched FLCL four times and still don't get it >.>
I don't think ANYONE is supposed to get it...
Read the manga. It explains everything...
(not)While I agree, Cowboy Bebop is a definately good primer to high quality anime - I always thought Samurai Champloo would be a good contender.
Just don't do what a freind of mine did - Don't start them off with english dub early Naruto. (Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it,Believe it)