I stopped Ayashi no Ceres after five or six eps, so I'd vote no on that. I'd also agree Princess Mononoke might be a bit harsh. Mushishi is very good, but can seem slow to some people.

Instead get Spirited Away. Classic story about a girl trying to save her parents from an evil witch, but very well done with creative animation. Won a bunch of awards too.

If you must go for a series, well, it depends on what she likes. I liked Ghost in the Shell (sci-fi, more adult/complex themes) or Kare Kano for a good romantic comedy or Paranoia Agent for sheer weirdness.