Trying to open, we have an unfinished basement....

[playfelt]

You could buy some of the blue tarpaulin type things or similar from home depot to cover the insulation - even though parents know it is behind there if they can't visually see it they will be better about it. Then you can use the tarpaulins for paint cloths or crafting or building tents, covering sandbox etc. so they aren't wasted. You could also get the type of curtains that have grommets at the top and put hooks in the top beam and hang them which would cover the entire wall. Then as you stud you can remove them a section at a time and reuse them elsewhere. You might find for quite awhile that it covers the walls enough you just live that way till you are truly settled. The floor covering is a must. The foam mats will be the fasted way to go. You can section off an area by placing furniture, shelves, bins around the matted area. Use one of the play yards in the open position to gate off the laundry area. I have some 16" deep utility cupboards I used when we first moved in to create a wall and then installed a gate between two of them. The cupboards gave me an instant wall and storage. You could consider doing that along your outside walls too meaning you have a lot less wall to cover since the cupboards stand 5-6 feet tall depending on style. Canadian Tire have some on sale right now. That means you will be able to stash a lot of stuff including non daycare items by tying doors shut. We had unfinished walls behind those cupboards for over a year before we finished them. I got child friendly fabric from the store and staple gunned it to the rafters to cover the top of the walls behind the cupboards. It actually looked really nice and was cheap and the good thing with the cupboards is they find uses in other places in the house or well you are always going to need storage in the playroom so even if you do finish the walls eventually you will still need the cupboards.