Anime recommendations?

You listed sad, tragic, and horror as your favorite genres, and you have Higurashi marked as a favorite. Watch Mahou Shoujo Madoka★Magica. Don't be put off by it's cutesy exterior, it's a dark show. It's not gory like Higurashi is, but it's just as intense. 12 episodes long. First two episodes are introductory, then things start to heat up in episode 3. I definitely recommend it.