In our basement we have two different framing setups that support our joists. Please see photos to help explain, but 2 of the walls have plate on the concrete foundation and 2 have for lack of a better term a small wall then the plate with joists on it. Any clue why this was done other that to save money? Also the small wall is insulated with fiberglass batting and covered with plastic. This seems to be leading to moisture and potentially mold issues. Any ideas what the plastic is there for? What is the best way to insulate this space, rigid foam board, spray insulation? 
Basement framing and insulation question
basementinsulationmoisture
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It sounds like you're saying your basement is heated, but nothing else is (possibly the floor above is exposed to the outside).
What you've done is put in insulation below the subfloor to try and keep the heat in the basement. This is a good idea, however, any time you have warm meeting cold, you're going to get condensation, and so you need a vapour barrier on the warm side only. This prevents the moisture in the warm air from getting into the cold zone.
If you have the vapour barrier on the cold side, you'll get condensation on the vapour barrier itself, between the insulation and vapour barrier, and this will lead to mold (and it's possibly a worse thing to do than have no vapour barrier).
If you have vapour barrier on both sides, you'll also run into trouble as if any moisture DOES make its way in between, there is no drying and no way for it to get out.
If you're using batt insulation, the best thing to do is put a 6mil vapour barrier on the bottom side of the joists, and seal it as best you can around the edges. Ideally you want a continuous barrier with no gaps. The vapour barrier on the ceiling should be connected to the vapour barriers on the walls, and then is typically sealed to the floor using acoustic sealant.
Foam insulation works as a vapour barrier as well, but you need to ensure all gaps between each piece and around the edges are sealed using air-tight tape (eg, Tuck tape).
Realize though that having this vapour barrier in place once you're finished construction will actually be detremental. You don't want to vapour seal between heated rooms, as it inhibits natural drying and air/moisture movement. If you end up having the basement unheated (or minimally heated), then it becomes the cold zone compared to your first floor and so your vapour barrier will be installed on the wrong side.
There is a rigid polyisocyanurate foam core insulation, often sold under the brand name Super Tuff from Dow that has a higher R value than XPS. It is R-13 in 2 inch panels and is higher if you trap a small air barrier behind it (around R-15).
The foam has a foil vapor barrier on the back.
You could
- mount this on the existing furring foil side out, using glue and screws
- seal the edges with foil tape
- reinstall paneling with glue and screws throught the foam, into the existing furring.
HOWEVER: The paneling could hold itself up when mounted this way, and you could mount lighweight things, such as pictures. The walls would NOT be suitable for mounting shelves, fixtures, heavy mirrors, etc. You would need to take care and inform any subsequent owner that the walls were not intended for bearing any signifciant weight!
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Best Answer
I'm no expert but sharing what I am doing. Using rigid foam r13 along studs exterior wall which is concrete. I used drylok extreme paint to water proof the porous concrete in my basement. It typically brings moisture in slowly but this should deter it. The 2" foam will act as my moisture and vapor barrier as well. The basement is typically controlled and should maintain fair temperatures. I am using drywall right on top with a 1.5" space between foam and drywall for breathing.