i think a golden neutral is the way to go. wool is the best for releasing stains, and a slight pattern helps (that doesn't detract from your fabrics). this is rug that we used in our client's home where Pucci, the 6 pound Maltese, is in charge :) it is from Surya and there are many variations/colors available.

Maybe something along these lines? All are from Wayfair.

You have 3 colors to use in selecting your rug. The rug can be solid or a combination of all three colors and can be lighter than those hues shown.

The room is very pleasant, but the two tables with buffet lamps don't seem like the right solution on either side of the fireplace.

Doggone those pets! Love the little buggers but they can wreak havoc on a rug. :)