Where will you put the sofa? At a minimum, the rug should slip under the front 1/3 - 1/2 of the sofa and extend past the ends of it by at least a foot. Keep it at least 12" from the hearth, 15-18" if you have the space. If I were you, the TV would go on the wall left of the FP and a 3-seat sofa would float facing the end wall. Art over the mantel, sofa table behind sofa, maybe room for a chair or two at the window side. Swivels could turn to watch TV.
Q