Almost any cat you get will shed fur all over the floor, carpet, and any other place where you don’t want cat fur to collect in little tumbleweeds. If the idea of constantly cleaning up cat fur doesn’t appeal to you, consider getting a cat with no fur or little fur at all.
The Donskoys are mostly a hairless breed from Russia, which makes no sense because Russia is a cold country. Another near harmless breed is the Lykoi. As long as you’re willing to adopt a unique cat breed, you can find a cat that won’t shed much, if at all.