Approved Sources
In general any published Wizards of the Coast book can be used for your characters in Dark Chaos games, unless a specific game or campaign has a reduced list for a particular story. Usually Unearthed Arcana (playtest material) or Homebrew (unofficial user-created) will not be approved, but check with the DM if you think there is a valid reason for a specific case to be allowed.
Starting Equipment
The starting equipment determined by your class and background can be added to your sheet, unless the game rules exclude it. Certain high-level campaigns or games (like Escape) will have special rules for starting equipment, so check the specifics for your game type.