I would use a slightly textured tile for traction. There are very good commercial sealers that work well. I would stay away from terra cotta tiles and slate - both are very high maintenance. My husband installed a beautiful slate floor at our old house, and I found out that it stains, even when it's sealed.
An alternative you may want to look into is something that's becoming more popular - a concrete floor that has been stamped to look like tile. I've seen some really nice ones, and they are a breeze to clean. No grout lines, very durable.