The best mystery I've ever read is probably Black Peter by Sir Arthor Conan Doyle. I haven't really read a lot of mysteries, so I don't have much of a choice. Of the choices I do have, I like this one because it is more than just a simple mystery story. The author was good at adding suspence to the story even though it is a short Sherlock Holmes story.
I think a good beginning to a mystery may be: "One stormy night, a suspicious figure ran through the nieghborhood."