Gloss tiles and any moisture will be slippery like ice. Black and white is a vlassic, but it’s also a high maintenance PIA type of floor as it shows every bit of dirt and needs constant cleaning to look good. It’s also a formal and traditional look that does not mesh well with what can be seen of your more contemporary and casual home.

Your tile choice should look like it belongs in the rest of your home, not like it Landed From Mars. A natural slate might be a better choice for a more casual woody Zen Modern type home.

We had high-gloss tiles like that in the entry of our last home. Slippery, especially when wet. And slippery in sock feet. I would not do it again.

Also, I'm having a hard time imagining it on the stairs in the foreground.

As far as the black-and-white? Hmmm . . . not sure. It's a formal look, like Sophie says. Is the carpet on the stairs at the right staying? It doesn't seem like it would play nice with the black-and-white.

Go with the same wood as the floors. You have both wood and carpet butting up to the tile. No need for a third surface in such a small area.

After wood is installed, stained and finished to match then look for a nice entry rug.

matte porcelain. i love black and white checkerboard but it looks best on the diagonal... otherwise it looks 'diner'. and i can't see how it would work with your step down.

my kitchen is matte porcelain.

Not polished and Not a fan of black and white pattern

i'm going to add, if you want to do your step in wood, rather than tile, than diagonal black and white can work for your entry but you gotta make the whole foyer more chic to support the look. every morning when i come down for coffee my kitchen floor makes me feel i should be wearing feathered mules.