First off, let me note that I am a tenant in this house. My landlord lets me do small improvements, but I'm not going to finish the basement with drywall myself.
Basically, we have an unfinished basement space in the house that is used for storage, laundry, and minor workshop duties. There are also some drainage pipes that are in the center of the room. The ceiling and wall areas are filled with pink fiberglass insulation, but they are open and exposed.
I'd like to make the space a little more inviting and perhaps a little safer to breathe in for extended workshop sessions, by covering up the insulation with something inexpensive and quick to install (and that won't require a construction permit). Is perhaps stapling Tyvek sheeting to the studs a solution that would work here? Any other/better ideas?