The only one on that list I watched is Angel Beats, so you could try and watch that if you want, but I also recommend you watch Case Closed.
Detective Conan is the intriguing story of Conan Edogawa, a little boy with his own share of secrets, and his adventures against the shady world of crime. Himself a victim of a crime of most unusual circumstances, he's formed a band called the Junior Detective League [Detective Boys] and is setting out to solve crimes, one mystery at a time.
At the age of 17, Shinichi Kudo was a high school detective. One day he was knocked over and fed an experimental drug that was meant to kill him. Instead, it changed him into a kid. To protect his family from the men that poisoned him, he changed his name to Conan Edogawa (which he pieced together from the authors Sir Arthur Conan Doyle and Edogawa Ranpo).