I read Manga more than I watch anime, but there is usually an anime based off the ones I read.
So, I'd say: Gantz
- Because it is extremely violent, sexual, and it has good characters. Its about a 15 year old kid who is killed in a subway accident but is brought back by a sphere only known as Gantz to hunt down and kill aliens in a sort of "game"
Death Note
- Because its a very intelligent psychological crime thriller about a 17 year old kid, Light Yagami, who's very smart (apparently one of the smartest in Japan) and he's bored. A death god named Ryuk, who's also very bored, "drops" a Death Note in the human realm and Light ends up getting it. The Death note allows the owner to write any name in it, while knowing their face, and that person will die of a heart attack or however the owner of the Death Note sees fit.
Those are my two favorite series. Now, if you want movies, I'd strongly recommend Akira and Ghost in the Shell. I don't have to explain it, just watch it. Even if you don't like anime, you'll love these movies.