If you're curious about how it all fits together, my signature contains a giant flowchart that pieces it all together. Don't feel like you have to read anything in particular, though - that list Sci posted is going to be brilliant reading start to finish even if you don't add anything else to it.
Be aware also that a lot of those books are collected in Twist Of Faith and These Haunted Seas, two bigger omnibus editions.
Oh, and you should also probably know that there's a huge time-jump before Destiny, where the DS9 narrative skips several years. There was some editorial changeover and it's not the smoothest of transitions. However: all the stories before are fantastic, and all the stories after are fantastic, and it's absolutely worth the journey. It'll just be better if you know to expect it going in.