I prefer girls as main characters and not some wimpy girl I guess but I have watched a few anime with wimpy girls. I like supernatural , action, romance ( I like a little romance in every anime but it isn't totally necessary), school comedy.
Anime I have seen/ still watching:
Bleach, Naurato, Vampire Knight, clannad, elfen lied, arcana famiglia , hakuouki reimeiroku (series), fruits basket, munto, say I love you, Cannon, my little monster, host club, soul eater, noragomi, fairytail, kotoura-san, samouri champloo, sword art online, pokemon , Hanayaka Nari, Waga Ichizoku, Psychic Detective Yakumo , brothers conflict, ghost hunt, Kamisama Hajimemashita , kurokami, Kamigami no Asobi Online , Hiiro no Kakera, Akatsuki no Yona, Mahou Sensou, Soredemo Sekai wa Utsukushii , Hidan no Aria, wolf girl and black prince, Otome Youkai Zakuro, free, toradora, nozaki-kun, angel beats, beyond the boundry, inu X boku, skip beat, magical warfare, Hanasakeru Seishonen, Sunday without god, neo angelique abyss, uta prince sama, sailor moon, maid no sama
Most Helpful Guy
Clearly what you want and need is Full Metal Alchemist Brotherhood (you might want to watch the non-brotherhood version up to episode 20 first to get acquainted with the universe and characters but not further because it is shit on the long term), and Baccano.
And there's Future Diary (Mirai Nikki) where the main protagonist is a wimpy boy who Is annoying as hell and his creepy psycho stalker "girlfriend" who is crushing on him and kills everyone who dares be a threat to their love.
I also vote for Steins Gate but it is not action.0