Covering exposed insulation

Our 10-year-old house has a basement utility room that our daughter is working to turn into an exercise room/home gym. There is exposed fiberglass insulation in the room, in two forms: On the exterior (poured-concrete) walls, fiberglass batting with a heavy foil covering has been fastened on, but some of the edges have the fiberglass exposed. In addition, the interior walls have insulation between the uprights; some is encased in brown paper and some is just exposed fiberglass. She of course does not want to be inhaling fiberglass fibers while she works out. There are numerous things to work around including the furnace/AC, water heater, water softener, battery backup system and electrical panels, and cable modem/hookups.
The question is how best to deal with this in a cost-effective way. I don't think that we want to build out walls and sheetrock over--that seems like overkill to me. The insulation in the interior walls could just be removed. Or Tyvek over? Suggestions welcome.