Durock, Wonderboard, and though I've never used it, Hardie has a backer board as well, it may be called Hardieboard or Hardiebacker...not sure.
They all come in 1/4 and 1/2" thicknesses. I always use half-inch, though I know many people use quarter-inch on flat surfaces...countertops, floors, etc...as long as the floor is stiff enough.
When you compare prices, don't just go by price-per-sheet, because all sheets aren't the same size.
You can use a marble saddle in the doorway to make the height transition as you go from one room to another.
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