I will be interested to see what replies you get since I was just at a carpet store this morning.
We are in the process of finishing off part of our basement and are looking for a neutral(sandy brown) color rug for the family room area.
Maybe you want to pick a color or pattern that will help hide any accidents.
My cat Samantha is 16 and she does save her hairballs for the basement or bathroom which has a throw rug which is easy enough to wash.
We also plan to put some linoleum down in the laundry room area where Samantha's litter box is too, so if she misses the box then it will be easy to clean up.

What rooms are you planning on redoing? Are they in the main living area?
I think it will be easier to find something for the basement since not too many house guests get to go down there.

Good luck and let me know what you decide on.