Hi Sixsticks,
I have also tiled over old tiles and it turned out great. The main thing is the correct adhesive for tiling over a smooth surface. A good friend of mine is a professional tiler he told me it would be fine to tile over tiles, both floor and walls. He said that’s what a lot of professional tilers do.
If the doors in your new home have already been hung you will most likely have to have some timber shaved off them.