Examples (and my personal favs that I can think of as of now) : Cowboy Bebop, Samurai Champloo, Steins Gate, etc.
I don't really care what genre as long as its really good and worth watching.
The numbers in parentheses are the estimated number of episodes
Madoka Magica is a really god anime, but it doesn't pick up till around episode 3. (12 eps)
Level E is super funny really good (12 or 13)
Baccano!! Is really good (22-24)
Durarara!! Also fantastic and you if like Baccano you'll like this or vis versa (25)
Romeo x Juliet is sad but worth it (24)
Princess Tutu is totally worth it and a little confusing at times (24)
Vandread is soooo good I'd recommend this if you like mecha (uh there two seasons of this but I think it's only like 26 eps in total)
Gurren Lagann is a must see anime both the dub and the sub are really good (again there's two season of this maybe 30 eps I honestly can't remember)
Trigun is always a classic anime (26? Maybe)
Princess Jellyfish is really cute (12?)
No.6 is def worth watching but there's some boys love in that so not sure if you'd like it (11?)
well ill give you some animes with 1-3 words descriptions
Alot of these are like romancy school life but i did add some action and horror as well
all are under 50 eps (most are around 13~30) except some of the multiple season ones
Ouran Highschool Host Club (Funny 11 episodes)
Kaichou wa maid sama (Funny+Romance+School 26 episodes)
Chrono Crusade (Action-Adventure+ Drama + Hints of romance 24 Episodes)