A dark gray porcelain floor tile would ground the mudroom and withstand all that a busy family would throw its way. Go for large tiles with medium to dark grout and small grout lines to make cleaning a cinch.
I'm not sure that there is a tile pattern which says 'classic' to me more than hex - I have it in my own bathroom and never get sick of it. Carrara has the gorgeous veining that will bring an elegant feel to a bathroom.
I'm a big fan of warm grays and this stone mosaic is no exception - this would be great as a kitchen backsplash mixed with whites or blacks or rich browns for contrast. It's warm without being too caramel.