Having recently renovated a place in the mountains I understand your feelings.
Do you trudge through this area in boots or shoes, or is it a slipper area?
Will you have floor heating?
If the answer to one or both is yes, I would remove the tile and stone and go for wood. It is so much softer and cosier underfoot.

We used recycled warehouse flooring in ours and left it raw for mud, dogs, etc.

We're about to change out the flooring in our mountain cabin also. After much research, we decided to install wood-like luxury vinyl plank in all rooms, including bathroom and kitchen. This product looks nothing like the old sheet vinyl - it looks deceivingly like real wood (except for some noticeable repeating patterns.) It's waterproof, very durable, economical, warmer than tile, and quieter than wood. I like that this flooring will be consistent throughout our relatively small space, and that it should hold up well to short-term renters who'll be staying in our place. I wish us both luck!