Insulation in already finished basement

Hi, Purchased a house a few months ago with a fully finished basement. Drywall installed on all sides. Carpet on floor in the main part of the basement. Finished bathroom has tile floor. Closet area on one side of the basement houses the gas boiler, hot water heater, and AC unit. The foundation wall is exposed in this closet area and gives some access behind the drywall installed about 1'-1.5' from the foundation wall. There is another closet at the back of the basement which gives some access behind the drywall installed at the back of the house. From what I can tell at the water shut-off panel at the front of the house, the front has soft insulation in at least part of the space. No access to the area behind the drywall on one side of the house. The rear and other side do not have any insulation in place. We use the basement as a guest room. OK in the summer, but gets cold in the winter. My also be affecting temperature on first/second floors of house since the staircase leading to the first floor is open (no door). I was wondering what my options are for insulation. It's my understanding that it's good to have some space between the drywall and foundation wall for air circulation in case of moisture. We had some efflorescence before that I've taken care of, so don't want to risk covering up the foundation wall and having mold grow due to moisture. Would be nice to make the space a bit more comfortable. Thanks in advance!