Insulating basement wall with 1" furring strips??
Is the room below grade? If so the energy loss isn't as great as above grade, because of the constant earth temperature.
@GBR - correct me if the above statement is wrong.
Thus if it were me I would get the 1/2" foam board cut it to fit between the furring strips then sheet rock over it. Depending on wall temps after that I would then use some 1/4" sheathing and install another layer of drywall. Just ensure it is all sealed up. With 1/2 board you have R3 and 1/4 sheathing you have R1 + two layers of drywall, 1/2" drywall is R .5, so R1. Only equals R5 but below grade is decent. However, I don't know if this meets Code in your area.
The bigger issue is what HVAC you want to use for heating and cooling, considering humidity and size.