I work as a colourist and the easiest method for a upmarket look is to choose an exact colour to match one of the colours in the tile. I would take the tile to a paint shop and get the colourist it match exactly one of the greys in the tile. Make the depth of the colour a light version. All white walls are on the way out. Lappatto tiles usually have some texture as they are semi polished. This is the latest look in tiles as they give a shine without the maintenance of polished porcelain which had been in. They are usually less slippery than satin or polished tiles depending on the brand.

I'm personally not a fan of tile - very hard on the feet, I find - so I'd probably restrict tile to the wet areas and go for hardwood everywhere else. Our last home had wood in every room except the bathroom, and after 10 years it still looked fine. Even the kitchen looked good. That said, we didn't have kids running around in the house. Did (and still do) have a dog, though. Our current house has carpeting in the bedrooms, engineered wood in the living areas, and tile in the bathrooms and laundry. All three floor coverings have a similar greigish tone, so to my mind they look fine together, and meet the practicality and comfort criteria as well.

I’d go with timber or cork. Cork is great in a kitchen. Easy on your feet and joints and things are much less likely to break if you drop them. Especially as you age, tiles cause fatigue if you are standing in the kitchen for too long. Cork is now available in lots of different colours and styles including charcoals and greys that might compliment your slate. It’s not all 80s orange. Of course timber can look great too. Just make sure it’s ok for kitchen use.

Since your tiles are NOT laid on a diagonal, they will not look dated. I would be concerned about the areas of floor that are used constantly. Eg: kitchen. Would the paint, overtime, be worn off. Laminate flooring would be good. If installing vinyl flooring, just be aware that the grout lines will show, if the tiled floor is not prepared before hand. You need to fill or the grout lines, so they are level with tiles. Maybe also installing an underlay before vinyl flooring. Personally, I don't mind the terracotta tiles. With the right wall colour and furnishings they look wonderful.