Instead of using a large amount of papers towels, use rags for cleaning and mopping up spills. Keep two storage containers in your kitchen or laundry room. One for throw away rags and one for rags you can use again after washing.
Cut up t-shirts - Use for the most dirty items and then toss them
Flannel sheets - Can be used more than once for light cleaning and dusting (wash afterwards)
Socks - Dusting. Put sock on your hand and wipe along blinds (you can use either wet or dry).
Towels - Cut up and use to mop up spills. Use on Swiffer cleaner.
Cloth diapers - You'll want to use these again and again so keep them for dusting and light cleaning and then wash.
Tea towels - Use for wet and dry cleaning or to dry surfaces after cleaning.