Without seeing the spaces and the materials, it's very difficult to help you.

Diana the fireplace is going on this wall in the living room pictured below. I have white oak flooring going in and doing white walls. We’re doing a wood burning insert stove. The living room is open to the kitchen that is going to have a mix of wood and dark green cabinets white countertops. This is the brick I would use thats in the mudroom

Unless you see the mudroom from the space with the FP IMO do what you love for the FP I will say all that light colored grout is going to be a PITA to keep clean in a mudroom

I think the brick vs stone choice is partly a regional preference. Did you look at existing homes for sale before you decided to build? What do people tend to do in your area?

Then it is a style choice. Stone will probably result in a more casual look. I don't think those are really your two only choices, either. Marble and granite surrounds are done, and tile is also sometimes used.

Have to agree with Patricia on the mudroom floor. Unless you have already had this type of floor and liked it, I would consider other options. Large format tiles are being used a lot now and the result is fewer grout lines. You can get something that is a slate look if that appeals to you.