Sectionals and loveseats trip up many a homeowner. A 3-seat sofa and a pair of swivel chairs are much more versatile. I would rework the large bookcase and have it wired for the TV which should be on an articulated arm for adjustable viewing. Place the sofa with its back to the frosted doors and two swivel chairs opposite with their backs to the double patio doors. They can turn to see TV or to converse with the sofa sitters. Add a large storage coffee table (for toys) that you center on the firebox. Then pull the seating 18" from it. If you want an area rug you'll need to do some taping on the floor with painter's tape to see what you need once the furniture is in place. I like rugs to slip under the front 1/3 of the sofa and extend past the ends by a foot or so. Keep it 12-18" away from the hearth. The swivel chairs will need to sit entirely on it to be able to turn. You'll need some lighting but I can't see where your outlets are. The fan light should just be turned on to see how to get into the room. Then it goes off and task and accent lighting come on to warm up the room and give it dimension and designate its purpose. Please include a smashing painting over the mantel where you already have accent lights installed.