Recommendations for introducing a girl to anime.

[Ryoku Slayer]

Since your friend is a girl, you should start with Shoujo anime. Here are some titles that she might like:

Fruits Basket
His and Her Circumstances
Studio Ghibli Movies
Fushigi Yugi
Ai Yori Aoshi+ Enishi
Love Hina
Angelic Layer
Someday's Dreamers
Ceres, Celestial Legend
Pretear
I My Me Strawberry Eggs
Ah! My Goddess
Memories Off
Sailor Moon
Marmalade Boy
Mahoromatic
Chobits
Sister Princess
One

These are my favorite titles and I think she might like them.