What are best anime's for teenage girls?

Ты should watch Bakuman. It's really good and inspiring. It's also pretty funny, and makes references to other Аниме like Dragon Ball, Death Note, and One Piece

Fushigi Yuugi
Sailor Moon
Mermaid Melody
Wedding Peach

I want еще action and Эмо Аниме and its kinda fun and enjoyable...

Ouran High School Host Club!! <3
Vampire Knight (my fave shoujo anime)
Акацуки no Yona (highly recommended!!)
Kaichou wa Maid-sama (perfectly fits ur ques)
Noragami (Бездомный Бог) (it has quite a few genres and is one of the BEST Аниме I've ever watched!)

Here were the вверх 5 Аниме that came to my mind when I read your question. And I bet Ты wont' regret watching any of them! XP

Ask for еще suggestions whenever Ты want!! ^_^

Check out sailor moon for girly action или squid girl for tennage-aimed comedy I personally would go for squid girl because it is really funny and original despite the weird name.