If you are seeking a truly open feel to the floor plan you have shared, then using one material in the mail living area is the best approach to making this space feel truly open. Using a variety of materials on flooring chops up the space and decreases the visual footprint. I would suggest using wood, tile, or if you are on a tight budget laminated flooring for the living/dining/kitchen. Then use carpet in the more intimate spaces; bedrooms and possibly hallway. Save the tile for the bathrooms.

Stacked splashbacks always look wonderful!

after watching my daughter and her husband agonize over the way their expensive timber floor has not held up well after 3 years, I would recommend tiles/wood look tiles with under heating. Their beautiful warm expensive floor looks like it always needs a clean and polish, not from neglect, they have cared for it well. One of the boards now has a slight and painful moan when it's stepped on :-( I grew up in a completely wood floor home and although it looked wonderful, my Mother hated it. ....and the mats ! Wood is a lot harder to maintain than tiles ,(no matter what the die hards say) the modern wood finishes are much better than they used to be.... But a piece of wood is rather arty no matter what it's used for and it does demand to be loved and cared for.....and if something goes wrong it's a lot more expensive to fix than sand and cement. Ultimately you have to be happy. BTW underheating tiles is warmer than timber :-)

Flooring should be light. I'm not sure how a bamboo floor would work. Did you end up going ahead with the kitchen plans? What did you go with?