And just to be clear, cork is wood so it has the same TONES as wood. That means you don't have to paint out the doors or trim. And cork can be used on stairs. You just have to find some generic stair nosings and you are done like dinner.
Here are my "budget favourites" with links to icorkfloor.com (USA) or cancork.com (Canada):
10mm Desert Arable:
https://www.icorkfloor.com/store/cork-board-floor-desert-arable/
https://www.cancork.com/store/floating-cork-flooring-desert-arable-10mm/
10mm Golden Beach (boring but gets the job done):
https://www.icorkfloor.com/store/cork-floors-golden-beach-10mm/
https://www.cancork.com/store/cork-floors-golden-beach-10mm/
If your budget allows for it, one of the toughest floors you will ever encounter:
https://www.icorkfloor.com/store/cork-floors-golden-beach-10mm/
https://www.cancork.com/store/product-category/luxury-vinyl-plank-cork-flooring/
The cork fusion is well worth the price. It is stunning, tough and can still have the insulating factor your are looking for.
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Cork floor links
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