In your climate, drywall should not be directly attached to furring strips on concrete. Warm, moist air in the basement will penetrate through cracks, outlets, around trims etc. When the warm. moist air contacts the colder concrete, condensation will occur. Because the space behind the drywall is basically "dead-air", moisture will be retained and rotting, mold etc will occur.
Generally, the following process is followed:
Attach barrier plastic to wall from one foot above ground level, to the floor, extending 10" out onto the floor. Studs or furring should not be attached directly to the concrete below grade level, but separated by the moisture barrier. (Vapor barrier and moisture barrier are the same - heavy gauge, UV resistant plastic sheeting. When applied to "part" of a wall, it is a moisture barrier. When applied to the "whole" wall, it is a vapor barrier.)
Install studs, or attach furring strips or metal Z-channels to concrete wall.
Install insulation - rigid foam board or press-fit batt insulation.
Apply vapor barrier from ceiling to floor. Do not trim excess at top yet (vapor barrier is generally 10' wide for application to an 8' wall surface. Caulk all joints where vapor barrier sheets overlap, and at junctions with window frames, door frames, other interior walls, pipes, etc.)
Trim vapor barrier plastic at bottom of drywall. Caulk the joint at the bottom so that the drywall, vapor barrier and floor gap is completely sealed. This sticky mess of caulking will be covered by a baseboard trim.
The header space / sill plate at the top of the wall and the spaces between floor joists need to be insulated and vapor sealed as well. Install insulation in all header spaces. Generally, batt insulation is easier to work with in these tight spaces.
Vapor sealing these spaces can be a bit harder. Idea 1 - use the extra few feet of surplus vapor barrier from the wall to extend up to the bottom of the floor, covering the insulation. Caulk and staple to the floor and joist. Idea 2 - Cut insulation batts to fit joist spaces. Wrap the batts in plastic (like you are wrapping a Christmas package. Press wrapped batts into place. The "force-fit" of the wrapped batts will provide a moderate seal to adjoining surfaces. If you have space to getting a caulking gun up there, caulk around wrapped batts. Idea 3 - Cut rigid insulation to press-fit into joist spaces. Please not that this is not permitted by many building codes as rigid insulations must be covered to protect them from heat and fire (unless squares of drywall are applied over the rigid insulation -a pain)
Generally, 3 1/2 inches of batt insulation, or 2 inches of rigid insulation is desired (or mandated). This provides adequate heat retention in winter, and a cooler, more comfortable basement in the summer.
More important, is a completely air-tight vapor barrier. Don't skimp on caulking. Seal as well as possible around outlets, pipes, window frames etc. Nothing will cool the basement faster than cold drafts coming in. Equally important, you don't want warm moist air passing through. This will lead to structural decay and mold / air quality concerns. You will also find the basement will be much dryer in the summer months.