I do not use a ground cloth under my tent. That's what the tent floor is for! Tent floors are, after all, quite washable if they do get muddy. I've never had silnylon floors soak through, either, even on a recent trip where there were several thunderstorms (think cloudbursts) each evening. It is quite important to select a site where you're not going to be in a lake in case of a hard rain. I learned that lesson the hard way; that was the same occasion when I learned that a sopping wet synthetic bag is no warmer than a sopping wet down bag. I have had (back in the bad old days when I packed a 5-lb. tent and put a ground cloth under it) water get between the tent floor and the ground cloth, which means you might as well not have the ground cloth.

If I were tarp camping, as the OP is, I'd want either a ground cloth or a bivy. I certainly don't want either my sleeping bag or my air mattress sitting directly on the ground. I like the GG polycro. You can get lighter and thinner and cheaper (1 or 2 mil painters dropcloth) but it is like handling plastic wrap.