Global Entry most certainly includes PreCheck. I've had it for nearly a decade.

But to the point, LGA out of DFW mid-Saturday, for a mainline domestic flight I would get there over a solid hour before the flight, assuming no luggage checking. (If there is luggage checking, you're on your own since I've never done that here.) Go to Mr. Google and memorize the TSA checkpoints, however, so that you know where to go even though non-PreCheck entries typically at least have a separate (i.e., shorter) line. My local knowledge reveals that Saturday morning in the summer can often be shockingly busy. Mid-morning may be better than early, which is when I've come. My main point is this: do NOT assume that Saturday morning won't be busy!

Sprinting from mid-terminal (PreCheck) to a low or high gate-number entry (non-PreCheck) to get a shorter line when you're up against a departure deadline is really unpleasant. I ought to know ...