I'd think ceramic tile and repticarpet would look lovely, I use Linoleum and paper towels for all my tanks, and that also works really well (I used to have tile but taking big heavy tile slabs out to hose them down each week from ALL the tanks was getting tiring for me, so I go with linoleum and it works just as well).
My reptiles and I do seem to really like those substrates the best. When I had Tile I would have Tile all over the floor of the tank, Then have sections with carpet or paper towels on top of the tile so my animals could burrow and they really seemed to like that.
In my opinion it's much easier to Keep the tiles loose, especially in the long run like if you're ever upgrading your tank or selling it or etc, It's much better to have the tile Removable so you can take them out and deep clean everything and if you ever change your mind you can switch out the tiles.
Mortaring them would probably look nicer, but also might be a bit more difficult for cleaning and such (see above paragraph). For mortaring the tiles you'd definitely have to spot clean a lot more. So it's up to you honestly.
Also, I'd love to see some photos of the finished project!