The new luxury vinyl is great for this type of thing and comes in slate looks as well as wood, and pretty much anything you can imagine! Slate or porcelain would work too, but you can save yourself a lot of money by using a slate-look vinyl.

I do wood for a living but I love the multi color 16" x 16" slate in my kitchen. I have seen a couple of fakes that look pretty good that are smoother and probably more practical than real slate but I'd rather have the real thing.

Optimally, a through body porcelain > followed by porcelain > ceramic > a quality natural stone > Unglazed porcelain or ceramic > marble > travertine. Your choice may depend on the substrate. Is this over wood framing or a ceement slab ?

I just put slate in my mudroom. I'll let you know how it goes. I think it's a beautiful material.

I also think it is beautiful but would be so hard on the feet (and back) in the kitchen!

I put slate in kitchen of a former house, and hated it. It's slippery as snot when wet, entirely unforgiving in disguising dirt, and a maintenance headache (resealing is absolutely necessary). Plus, if you don't have an installer experienced in slate instillation, irregularities in the material itself make it likely you'll feel the sharp edges along the tile. It was always uncomfortable to stand in bare feet. My current home has ceramic tile, it's much more forgiving in all ways. I may change it in next few years to a porcelain tile, but never again will I choose slate.

It's funny how experiences and opinions differ. My wife would be mortified to see me publicly admit that in the first several years with our slate, we rarely cleaned the entire floor at once, were nonchalant about ice cubes and water sitting on the floor, had a macaw that made a mess on it almost daily and we didn't reseal it until it was almost ten years old, yet it never looked bad.

We just put groutable LVT tile down in our basement bathroom and I love how it looks. Just staring at it, you can't tell the difference between that and regular tile, although from certain angles if does look a bit plastic-ish We put it down because of humidity issues and an uneven concrete floor. I'm not sure if it would look or feel different on a wood subfloor though.