10x12 your only lookin at 3 sheets of drywall if you use 8 footers for each wall, 4 sheets for 10 fters for the ceiling. A couple boxes of 500 drywall screws, a good friend and half the morning and youll have a safe and finishable space for your children to play. Even if you dont tape and float it it will be better than the fluffy pink stuff.
Btw, if they do get in it, masking tape is your best friend...stick it to the spot that is ichy and peel it off. It takes all the fibers with it, and in a couple mins no more ichy.