This is your last chance to insulate, so take the opportunity.
First, finish only dry basements. Moisture trapped behind walls in finished spaces poses health issues. Dry basements are the only healthy candidates for finishing.
At Mosby Building Arts we like to apply Xypex or Dry Lock moisture coatings to the dry, raw concrete walls behind the planned wall framing. This provides a reasonable moisture shield from the porous concrete foundation walls.
Insulation can take several forms. The first is a rigid insulation of extruded polystyrene like the blue DOW Styrofoam or the pink Owens Corning sheets glued directly to the Xypex or Dry Lock coated concrete foundation walls. Next is to frame the walls and insulate with un-faced, fiberglass insulation. Use NO vapor barrier with the insulation or wall framing system.
NO polyethylene plastic, NO Kraft faced paper backing on the insulation, NO vapor barrier on the walls covering the concrete. This allows the wall system to pass any moisture out of the wall which means it will allow the wall system to dry out. Then apply your drywall or finish wall system.