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.

Get the professional sander guys in to repair the living areas and kitchen but don't go too dark with the stain as it will kill the lovely grain in the matai. I'm thinking a couple of tones richer than the timber knots showing in your photo, definitely no yellow tone at all. In NZ stepping on to carpet especially in a kiwi winter is so much nicer than a cold floor board shock!!! A nice area rug for the lounge and you're done.

We had the same issue in an old kitchen, we went with Coopers, There is a stripper then wax that will soak in. The stripper is in spray bottles, but I'd send the dogs on holiday or keep them outside while you're doing it. It'll take some elbow wax, but will look amazing when you're finished. Good luck!

Why Floors Should Be One Of The Most Important Investments When Buying A Property | HARO Flooring New Zealand