Your room seems to be gray and greige, but the new rug looks to be off-white with a navy and yellow pattern. Look for pillows with those colors. Choose patterns or solids as long as the colors match the rug. Look for curtains that pull the color up onto your walls. I prefer contrast in my decor, so I show a navy that would stand out from your walls. And, look for some art for opposite the curtains that contains those colors.

Try removing the throw pillows for a week to see if they are really needed. If you do actually use them, try some reddish pillow covers from the reddish color in the rug.

As you can see, the verdict is "no rubber backed" anything with hardwood. Just because you move them around doesn't mean they won't damage your floors. Rubber has petroleum based plasticizers that keep it soft and malleable. It's the plasticizers that cause the damage. The petroleum based stuff is very damaging to polyurethane (which can be petroleum based as well). And that's where things go sideways. Even to 'solid state' products can and will have chemical reactions to one another. It just takes a bit more time to do it..that's all. I would ASSUME the rug backing WILL damage your hardwoods. That's the safest way to look at this. Go ahead and go rug shopping. These other rugs are going to be used in other areas...where stone and tile have remained.

Love the new floors. The staircase makes the rug placement a little awkward. I don't think round will work, the space is a little tight. I think 4 by 6 is a nice compromise between a too-small rug and one that it is slightly too big and ends awkwardly by the stairs.