I would do slate, hands down. So cute for that space!

https://www.houzz.com/products/cabot-slate-tiles-montauk-blue-natural-cleft-slate-natural-12x12-prvw-vr~81410274

https://www.houzz.com/products/natural-janeiro-slate-tile-montauk-black-12x12-10-sq-ft-prvw-vr~79370769

https://www.houzz.com/products/pennsylvania-bluestone-pavers-natural-12x24-sandstone-hardscape-50-pieces-prvw-vr~79378498

I agree with Carly that slate would be beautiful. I also would never use it :). I have had it before and wouldn't go there again, especially in a mud room, because:

1. It shows EVERYTHING, especially in mid to dark colors. Every dog hair, dirty footstep, slush/salt residue - everything. I can see by the cubbies that you have kids, and I'm guessing lots of dirt ends up on your floor.

2. It is generally uneven - lets face it, some of the beauty is the unevenness of the stone surface. This allows dirt to accumulate is all the three dimensional uneven spots, and it is a nightmare to keep clean. It looks bad within minutes of looking good.

I actually would consider a wood floor if you can - I have one now and it's actually quite easy to clean and looks beautiful. Or if you prefer tile, choose a wood look tile - there's great ones available these days.

Brick is really unique