It is very common in the US to use foam boards with z furring channels to insulate agaist concrete or similar materials, but using furring channels with just about any type of insulation would work (foam is the most efficient, though). You can then fasten drywall or your typical wall covering to the channels and paint as normal.
Just about any solution will reduce your occupiable space though, or protrude on the exterior. Most jurisdictions in my area are ok with encroaching a few centimeters for the purpose of higher energy efficiency, but I have no idea about your situation.