Hi Clairetta! Welcome to the forums. I have cats too...3 of them and a chihuahua, so I've experienced the frustration of what they can do to flooring. I've had to replace the carpet in 2 rooms. I chose vinyl tiles because they were the least expensive and easy to install. We are selling our home, we so weren't looking to put a bunch of money into it.
My personal preference is cork though. It meets all of the requirements that you are looking for. Be careful what you buy though. If you choose cork, check out this guide to make sure you get a qualiy product. Less quality cork floors may not hold up to your cats
www.findanyfloor.com/BuyingGuides/... Hope that helps! Look forward to chatting