Lovely colors...all of those!
John, It doesn't happen very often but you got correct answers from the flooring department at your HD. (was it Mad. Hghts?). Well....with the exception of the steel wool recommendation. I recommend scuffing with a Carborundum brick or with 60-80 grit on a belt sander. Then super clean and rinse.
Use a high grade latex modified thin set mortar (bag), to set tiles. Do not use polished marble. Also do not use a tile that is too rough or textured. Matte finish smooth or with slight texture is good. Black will not be easy to find.
All this is contingent on the old floor being in good condition. Remove the toilet, and pedestal sink, if any. Do the walls all have tile with a base molding at the bottom? Is the marble threshold high enough above the floor?