Most timber stains will look good but I would go for a mid brown stain. Look at kitchen photos here on house - search white kitchen with timber floors. I just checked myself - when you enter white kitchen and timber floor- the majority of photos have medium tone (35000 images ) and only 15000 images or for dark timber and even less for light tone timber.

It doesn't look that bad. I'd go with rugs inside and out to draw your attention away. If you go with a stain, you can get grey stains. Bunnings have a Hunter Grey.

Contact a flooring installation specialist and get them to meet you on site. There are too many products on the market now, so it can be too confusing.

We found a tile expert who was able to clean the tiles and remove the stains using a magic eraser. before this the tiler was going to rip them up and replace them as they couldn’t confirm how to remove the stains. The tiles are gloss porcelain.