Definitely not the natural gray. If you are okay with the grout lines looking more prominent on some of the areas of the tile, i would do new taupe as it will hide dirt/stains better.

I would go lighter than the mushroom, something that will blend in and not create its own criss cross pattern on your floors or detract from the beautiful pattern of tile.

you might want to take a look at darker like "Mocha" or "Coffee"?

All too dark. Antique White. It will get darker over time.