What are best anime's for teenage girls?

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

Fushigi Yuugi
Sailor Moon
Mermaid Melody
Wedding Peach

I want 더 많이 action and 이모 아니메 and its kinda fun and enjoyable...

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

Here were the 상단, 맨 위로 5 아니메 that came to my mind when I read your question. And I bet 당신 wont' regret watching any of them! XP

Ask for 더 많이 suggestions whenever 당신 want!! ^_^

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