The best Mystery I have ever read is "The Speckled Band" by Sir Arthur Conan Doyle. I like it because it was the first mystery story I read. Also, it keeps you wondering how to solve the story. Sir Arthur Conan Doyle did a great job with all the Sherlock Holmes stories.
I think a good mystery starter would be: One foggy day a tall, skinny women with long nails that were black, was suspected for kidnapping children.