Your question is a very vague one. I need more information about what kind of story/genre does your sister prefers before I can list anything down. A 15-years old girl can have all kinds of preference ya know.

Barakamon, Nichijou, Working!, Gekkan Shoujo Nozaki-kun for the comedy part.

Topping off Rei7's recommendations and listing based on given genres plus the fact that they're to be recommended to a girl:
[Fall 2013]
Kyoukai no Kanata, Nagi no Asukara, Golden Time, White Album 2 (No direct relation to the first season), Magi: The Labyrinth of Magic, Gingitsune, Non Non Biyori, Galilei Donna, NouCome (The original title is bloody long)

[Winter 2013]
Noragami, Toaru Hikushi no Koi Uta, D-Frag, Chuunibyou demo Koi ga Shitai, Silver Spoon, Mikakunin de Shinkoukei, Inari Konkon Koi Iroha

[Spring 2014]
selector Infected Wixoss, Bokura wa Minna Kawaisou, Sore demo Sekai wa Utsukushii, Isshukan Friends, Black Bullet, No Game No Life, Ryuugajou Nanana no Maizoukin

There's a lot more to list down but I'm sure these will last her for quite a while. I'm sure you have seen the names of some series while others are complete stranger to most but I'm listing down based on the information you have given. None of these series are bad, mediocre to some at worst.

*No horrors. All listed are comedy, fantasy and drama series. There haven't been good horror series during these 3 seasons.

I would recommend:

Love Lab http://myanimelist.net/anime/16353/Love_Lab

Non non biyori http://myanimelist.net/anime/17549/Non_Non_Biyori

Kiniro Mosaic http://myanimelist.net/anime/16732/Kiniro_Mosaic

Gochuumon wa Usagi Desu ka http://myanimelist.net/anime/21273/Gochuum...a_Usagi_Desu_ka

these are my favourites:
-Yakitate! Japan
-Beelzebub
-Nanbaka