I'd just go with whatever you can find at lowes/home depot for the ground cloth, it's not a technical/backpacking tent that needs lightweight or expensive, etc.
ETA: I went to check what I use on my big family car camping tent, it's just a 10 mil grey/brown tarp from lowes. I use it for other stuff around the house too. I have a fitted ground cloth on my smaller tents.
I have had great luck so far with my 12' x 12' kelty noah's tarp for a shelter, it is very versatile, and cheaper than most tarps of similar quality.
One word of caution, big tents like that (I have one too for car camping) are not designed to withstand heavy amounts of rain, so I would plan your trips for fair weather if possible.
I use a grill similar to
this one when car camping, works pretty well.