You didn't mention whether you intended to turn the below grade space in to a family gathering area or if you intend to leave it unfinished for now.
So let's assume you will not be finishing the space for occupancy now but might later.
Insulating foundation walls
You have several choices:
- You can build a stud wall adjacent to the concrete wall and install fibrous insulation between the studs leaving an air gap behind the wall. You could glue a foam board insulation (with a Class 1 fire rating) directly to the concrete.
- You could opt to spray a closed cell foam insulation directly over the concrete and cover to meet local building codes.
- Or you might attach furring strips to the foundation walls and insulate between them with foam board insulation.
Insulating for habitation
If you intend to finish the room for habitation I recommend continuous foam directly attached to the concrete.
- You can build a stud wall in front of the insulation later.
- The foam board will act as a vapor barrier to prevent wicking through the concrete.
- I recommend a minimum of 2-inches of foam to prevent the surface of the insulation from reaching dew point.
A world class product for this use is DOW Thermax. Great product and fire rated too. Check out this video for further detail about this product.
For more information:
Read "What type of board insulation is best to avoid basement moisture issues?" a Q&A answered by David Edwards.