Your moisture issues are going to be a problem whatever type of insulation you put behind the walls and on top of the strapping. If this is going to be living space on the inside of this wall and you have had moisture related issues on this wall before, than you are doing yourself no favor by putting any money into the wall until you deal with the drainage and water infiltration issues. If the wall is going to be below grade, the best way of dealing with it are to put a drainage system on the outside of the wall, using a system of waterproof membrane(usually asphalt based), drainage plane material(Miradrain) and a French drain with a perforated, sleeved pipe draining to daylight or a sump pump. If the wall is going to be above grade, then a simple water proofing membrane with a covering over it, like siding or stucco, to protect it from UV light degradation from the sun. If you cannot get to the outside of the wall, then install a drainage board on the interior of the wall that drains to a perimeter drain and an interior sump. While this is a chapter in and of itself, the point is that without getting rid of the water first, everything will turn to mush, you will have major mold issues though out the space and the associated health issues that go with sick building syndrome. Remember, all you need for rampant mold growth are air, water and a carbon source(anything that used to be alive(ie- paper(like on the outside of sheetrock) or wood(studs), cardboard, etc.
Once you have dealt with the water issue, the best foam board for insulation in dry spaces is polyisocyanurate rigid foam. It has a stable R value of 6.5-7 and is twice as good an insulation as polystyrene. Tape the seams between sheets with tyvek tape or stucco tape and install a stud wall over the abutting sheets to allow for the installation of electrical and sheetrock. Remember to make any wood touching concrete pressure treated. This system will give you a much more insulated space than any other insulation except Spray on closed cell polyurethane, which can be significantly more expensive and you can’t do it yourself. Polystyrene, R -3.1 is better in wet environments, like under a slab, but the backside of the walls to this living area should not be wet, right? Fiberglass will be less expensive, but less effective as well. Good luck.