Be careful. Touch nothing without protective gear, and clean up as the job proceeds. Lift nothing heavy, and remember everything is sharp.
If possible, stack like items with like items. If pieces of the structure are still intact, leave them. Be smart about what is taken apart and what is left. Smart demolition saves money. This is surgery, not demolition derby.
As the debris clears, wiser decisions can be made as to what needs to be replaced and what can remain. Pay close attention to wiring, pipes, and fixtures. In many cases, fixtures can be salvaged with a modest amount of care.