I have always used flat washers and screws - the really big metal washers, I think they're called "fender" washers at the hardware stores. The screw holds the washer tight against several of the squares in the hardware cloth.
Hope this helps.
I have transmorgrified a playhouse into a grow out coop.
I highly recommend you raise it on a platform, so you don't have to bend over to clean it. I put mine on a "foundation" of up-ended concrete blocks, with a pallet on the blocks, then plywood over the pallet for its floor.