I recommend Death Note because the quest to find out who is L and who is Kira is very fascinating. The story starts out with Light getting a Death note and he starts executing criminals by writing their names in the Death note. As there are more suspicious death caused by Light. The police gets suspicious and hires L who is the world famous detective to figure out who the killer is. Light decided to call himself Kira to hide his identity. You need to watch the Anime to figure out what comes next.