Insulating existing basement wall
Much depends on the dryness of your basement.  For most basements, worthy of being made into finished living space, 3 mil. plastic sheeting between the framing and basement wall should be sufficient for this already framed room.  The seems can be stapled to the inside of stud bays.

I'm not a fan of fiberglass batt insulation in basements, due to potential mold and mice issues, and, therefore, prefer XPS; which you could use for the yet to be framed rooms.  

Some might suggest foam board between the framing and drywall but I don't care for drywall to be hung on the required, longer drywall screw.  I guess it depends on the thickness of the foam board one uses.  A heated basement shouldn't require much additional insulation as long as the rim joists are well insulated.