The absolute lowest cost material is corrugated cardboard. Large appliance cartons would yield sheets more than adequate to cover the sides of these, and you'd simply tape them to the upright corner brackets. You could probably make "doors" with the stuff too and hinge them with tape. Plastic sheeting is easier to manage, though if it's tearing buy a thicker product and reinforce the "magnet" spots with clear packing tape.

Rudimentary dust management is easier and cheaper than you may think. A box fan with a cheap furnace filter taped to the side of it will catch a healthy percentage of the "random" airborne dust which is what's giving you the most fits. If you are out there while this dust is being generated, you'll benefit from a health perspective as well as cleanliness because fine dust is not great for the lungs.