There are those that baby new cars even if it is a Wranlger and then there are those who just can't wait to go off road with their new JL like Dick's 4x4 Garage. He wasted no time after putting on a set of 37's from a K10 Crawler to hit the trails and it pretty handled everything like a champ. The tires definitely makes a difference, so an aftermarket set may be a wise investment.
Well yea, larger wheel sizes will use more fuel because of the increase in rolling resistance and they're deflated for rock climbing. But you always bring an extra jerry can full of fuel when you're off roading anyways, so not really a concern.