To me, the current rug looks very monochromatic/brown in a very brown room, but if you like it, then it might be fine. I would love to see something with more colors to liven up the room a bit. Not sure any of your other choices are perfect because I don't think they meld the colors in them with the browns in your room. I think the size looks fine, but think you could also have a smaller one if you placed your furniture a bit closer together. (this might be camera angle). It looks like no one can reach the coffee table easily, from the couch or chairs and the chairs seem a bit far from the couch for a conversation area. I like the blues but would like to see a rug with some brown along with the blues (or other colors)... maybe along these lines.

The chosen rug doesn't play well with the furniture IMO. It's very stark against the brown sofa. It has a look more suited to a glamorous bathroom to my eyes. I understand not wanting to compete with the counter, but I think if you can return or use the white rug elsewhere, there are much better options for your pretty family room. It's a bit too small as well.

Sorry, not sure why the picture didn't post. Here it is again. RL, I like the round pendant and the pleated one in your first set of suggestions. Is that a Nelson bubble pendant? Also, I should have given a few dimensional details. The table is 36" wide at the ends, 40" wide in the center. Ceiling height is 92".

8 x 10 would be best, but turn this one the other way before you buy a new one, or turn the table. 9 x 12 is going to be too big. I have a 13 x 13 dining room and it has an 8 x 10 rug. To be honest, if I had to do over, I'd get a round table!