Check Menards or Home Depot like stores for the rubber mats. It'll be cheaper than buying a stall mat and cutting it.
If you end up using plywood, get a very good paint and seal the wood before installing it.
My two barn storage units, one safe, one metal cabinet, are bolted to the barn walls. This may be another option for you.
Inside Every Bright Idea Is The 50% Probability Of A Disaster Waiting To Happen.