I was just checking out a product called Mannington Adura; a luxury vinyl that is installed in 6, 12 or 16 inch 'tiles'. I was curious about heating the floors and the man at the store said you could lay heating mats with these vinyl tiles. By the way they are thick and not floppy like you might imagine vinyl to be. I really don't know much more about this product but I really like the look (like real stone) and the fact that you don't have to have grout and it feels much nicer than tile or stone. So this is a product you may want to check out.

And you can pretty much treat it as a neutral. Although it's dominating the room now, by the time you get your furniture in place and maybe a rug, it will fade into the background.

Have you spoken with your realtor about this? Honestly, giving cash back at closing for a floor allowance is appealing to a lot of buyers. Especially if you plan to live there while this work is done this may also be appealing to you - because, solid hardwood everywhere (except the bathroom with a tub or shower) is the most desirable for a buyer. I wouldn’t even consider a whole home in LVP as a buyer. Studying comps with your realtor and weighing that with your floor estimates should be considered. Feathering in new solid hardwood and sanding and staining may be the most cost effective if you have a decent amount of existing hardwood. If you are set on doing it I’d price three scenarios: feather in new hardwood and sand everywhere and stain, new engineered wood floor everywhere and new LVP everywhere (all in a very light medium brown). With the LVP you will have to put down new plywood everywhere which really brings the cost of that up so you may be shocked with the pricing studies.

I wouldn't do a wood ceramic tile next to your flooring. It might be close but not the same and it will clash. Pick a plain colour, one of the colours in your wood flooring, in a large tile. Looks like you have some grays and beige (not a pinkish beige) in your flooring so pick one of those in either a 12 x 24 inches or 24 x 24.