I myself would just put the tile directly onto the cement floor. As for the shower should you decide to use a subfloor like meford said theres no point in it. If your doing an old school shower your going to need to slope the bed anyway. If your doing new school (Schluter Kerdi) then you do infact need a somewhat level surface but the kit itself takes care of all this as the base is set into cement so you level at this point.
I myself like to mix the kerdi + old school way (make my own mud base) becuse it cuts about 400 off the cost of the shower, but adds complexity and margin of error.
I myself like to mix the kerdi + old school way (make my own mud base) becuse it cuts about 400 off the cost of the shower, but adds complexity and margin of error.