what type and condition of wood is your joist in, and what is the unsupported span distance of your joists ?

With those in combination with your other joist information you can calculate your floors deflection ratio (which needs to be within L/360 of the span for porcelain ceramic).

Ditra is by far superior to hardibacker, however hardibacker should work fine.

go with at least 3/4" of plywood.

Agreed... and what are you having to transition to?

The house was built in 1980 - the joists are in good condition and feel very strong. The total span is 13 feet.

I have to transition to wide plank tongue & groove pine flooring. The pine flooring is 3/4" installed on 1/2" plywood subfloor. I am aware that my tile will probably be higher than this, but I guess i will have to accept this...