We had the same problem and decided against a rug under the pool table - looked "off" and we were worried about people tripping on the edges of the rug as they moved around the table. We also have two chairs to the side and did put a rectangular rug under them. We're really happy with the final result. One thing that definitely helped us - foam squares that link together. I think we got them at Target. Using those we were able to outline different rug sizes in every room before actually making a purchase. Very helpful in our decision making.

Rug size depends on the kind of furniture you use. I prefer short legged sofas sit with their front 1/3 on the rug. Leggy chairs look better entirely on it, and swivels need it under so they don't wobble when turning. If you have a very large room, you can use a rug that will allow for all the seating to anchor entirely on it like an island for conversation and TV watching. Minimum would be 2 feet wider than the sofa and long enough for the chairs to also be on it. Keep it 12-18" away from the hearth. Painter's tape on the floor is your helper, and you'll be able to see how close your furniture arrangement brings you to a standard size rug that gets the right look for your room.

How large is the TV? Will it fit over the mantel or will it hang off on both sides? You can switch sides with the two chairs in front of the windows and the sofa against the wall. You don't have many options because this isn't a large room and you must consider the entry and other openings. You will probably want drapes or some sort of window coverings like Roman shades. It isn't a big deal that the furniture overlaps the windows.

Have you tried putting the couch in front of the windows? Put your chair where the couch is but slanted a little toward the couch. The end table and lamp could be beside the chair but on the left side of the chair. Then you might have room for a coffee table in front of the couch. It looks like the rug should be the other way but only you can tell that. Pretty room.