2. Mirror Universe
3. Vaughn Background
The MU anthologies I've read are pretty well-good; Obsidian Alliances and Shards And Shadows. The Sorrows Of Empire is highly recommended, too, along with Rise Like Lions and, if you don't mind a break from continuity, Dark Mirror.
Vaughn Background: Hands-down the best books for that are Serpents Among The Ruins and The Art Of The Impossible. (I can't speak for the DS9 relaunch, I've not read it yet.)