It looks like you have narrowed it down to some great options. I would go with lighter tone on the floor to offset back vanity. Depending on how deep is the black and how light is the grey, your grey choices could work too. Think if you would like a lighter look or a bit heavier. I hope this helps - best of luck - this will look very pretty!

stark black tile shows everything, aka dirt. You are better off with gray

Also, btw it doesn't have to be white, black or gray. It can be any color with black and white, such as blue. Blue with silver would make it pretty. Let me know if you're open to this

I like the different gray planks. I'm almost doing the same colors in my bathroom remodel. I'm doing the 3" black hex for my shower floor. Carrara herringbone on the bathroom floor (which btw, would be a great pic for you too) or, have you looked at the cement tiles? Here are mine, shown w/french oak flooring. (I did the oak flooring on my vaulted ceiling and am doing the black/white cement tiles for one wall in my shower. If I had more, I would have done them on the floor).

other options..white basketweave or black basketweave

I really like either one. That blue is pretty, especially if you have a white cabinet and tile. If you look up encaustic floor tile on here, there are plenty of pics. Try Pinterest too. show him some of those. I've also see ceramic look alikes, but don't know how they look in person.

I like the basketweave Beth showed. I also really like the tile just posted in black and white.