Rigid polyiso or extruded polystyrene boards can be used to cover the basement walls. When building a basement, you have to think about molds, air seals, and rim joists. Another great alternative is batt insulation. Batt insulation is made of fiberglass, mineral wool, or a combination of both to insulate the floors, walls, and ceilings.
Foam boards are inexpensive and great for insulation especially when the walls of the basement are ready. The foam boards come in industrial precut sizes and are easy to install. They are sealed in place with adhesive sprays and caulk.
Double brick walls with insulator material such as rubble, hemp, or wool trapped in the middle create the best insulation. When you are in the process of building a basement, make sure that you insulate the basement walls and air seal them.