Approach 1: Embedded. You can use storytellers to re-tell the traditional stories INSIDE your own quest or mystery. For an example, see Shadows of the Ishvara (where the Hindu gods tell stories to our hero as he journeys to find answers to his questions) or Lost in the Woods (where people search for a lost girl in the woods, telling stories to each other as they do so).
Approach 2: Reenacted. You can also use the traditional stories to provide the quest itself, so that the plots of the old stories become the plot of your own quest or mystery. For examples, see Odysseus Goes Shopping (where Sam, our modern-day Odysseus, experiences adventures strangely similar to the ancient hero) or Finals Week: Death Notes (where an OU student encounters supernatural creatures on the OU campus, starting in Bizzell Library).
Either approach can work really well, so figuring out which of these two styles you like best is the first question to ask yourself if you are thinking of doing a Storybook based on some kind of quest or mystery. So, take some time to look through these past Storybooks that feature some kind of quest, mystery or adventure, and see which ones you like best.
That will probably give you some ideas for what you want to do with your own project. If you are thinking you want to use some kind of detective, you can find plenty of Storybooks with detectives who are investigating a mystery of some kind!