We also have a tiled staircase with stainless steel strips on the edges. Yes, the joints are not all in alignment, but I actually think that looks quite nice. It perfectly matches our flooring, which consists of the same tiles in the basement hallway and the ground floor hallway.
Unfortunately, I no longer remember what we paid, but according to our tiler, "custom-cut natural stone" or tiles with leveling compound beforehand are roughly the same price. (For natural stone, the stone is more expensive and the labor time is shorter; for tiles, the tiles are cheaper, but the labor time is longer because the stairs first had to be brought to the correct height with a leveling compound before tiling.)