Recommendations for introducing a girl to anime.

[Japschin]

Get her to watch Fushigi Yuugi. Most girls I know like the series.
Angelic Layer
Azumanga
Ceres Celestial
Fruits Basket
Mahoromatic
Pretear
Tenchi Muyo Ova + Universe

There are more but since she's just starting out, give her some light stuffs.