Get a dehumidifier down there ASAP and get the relative humidity under 60% to limit surface mold from growing while you work. Anything that you can remove before you start gutting will help as will setting up room air filters/cleaners while you work. Bleach will kill the mold, but won't prevent it from returning. Keeping the RH below 60% will.
The sooner you can get on the gutting project the better, even if it's just stripping the lowest 12" of gypsum to allow any enclosed cavities to dry quickly, halting/slowing the spread.