Just be sure you size the ground cloth to be slightly smaller than the tent floor, so that water dripping does not pool on the up-side of the ground cloth.
I use tyvak. I actually scrounge it from construction sites for free. I even wash it in the washing machine after a trip if it gets really dirty. As Tyvak gets older, it is not actually waterproof, but still does the job of protecting the tent floor from pokes from sticks.
I find that those sharp pods from pine trees more damaging than rocks. And I hate to get pitch (sap) on my tent floor.
And speaking of pitch, do not set up a tent under a tree that is leaking sap!