This serves the same purposes as the white linen table cloth at the steak house back in the civilized world - it covers up whatever unknown lies underneath. At the campground, you can see what's there on arrival, and it isn't always pretty. So using this inexpensive bright red-checked vinyl table cloth will be a lot easier than trying to clean up after the many crews that came before your family.
The cloth is 72" x 54", big enough to cover up most tables. There's no heavy backing on this inexpensive version, so it may want to slide around some. Once you set the stove or plates down on it though, it ought to stay put. For 5 bucks, it's cheap enough to use it for your current trip and pitch it when your camping trip is over. Or if you're a tightwad like me, hose it off at home, let it dry, throw some character-building duct tape on the inevitable tears and use it again next time.
We have lots of other cooking and comfort items you can rent and buy to make the transition from your home to the campground a little easier:
Buy general camping accessories package - Towels, toilet paper, matches, paracord, first aid kit and more
Rent a portable camp shower - Get the grit and grime off
Rent a privacy shelter for shower or bathroom - Get the grit and grime off in private
Rent group dining serving utensils and supplies - spatula, tongs, can opener, extended fork, serving ladle, etc
Rent cast iron skillet - Great for like, frying stuff
Rent stainless steel pots - For boiling water, soups, pasta etc
Rent propane stoves - Crank up the heat for frying and boiling
Buy dehydrated meals - Just add boiling water. Better tasting than you might think
Rent a really awesome cooler - When the ice store isn't nearby, this does the trick