Any of the above will work, but the subfloor has to meet minimum standards of support. After taking out all the old tile you should be staring at a minimum 3/4" plywood subfloor. If not, if its plank it needs to be covered by a minimum of 1/2" plywood, screwed, not glued, every 8". All of the underlayments you mentioned will require being embedded in troweled thinset. Hardibacker would be best if you still need a little more height on the floor prior to tiling. You can use the 1/4" or 1/2". The thickness only comes into play for added height, the board is not structural at all so going thicker wont beef up the floor. You should also check the floor joists to see if they are capable of dead weight load bearing. I'm sure they are if you already had two layers of ceramic on them with NO cracks in the tile or grout.If there was cracking, better check with an engineer type before going ahead, or you will be seeing the smae cracks again in the new tile.
The mats are easier to work with and cut. The DITRA would use unmodified thinset over it to set the tile, pretty sure Stratamat is the same but not positive, Hardi should have modified thinset over it to set the tile and it needs the seams taped with fiberglass mesh tape. I use a lot of DITRA, the Stratamat is not readily available by me so I go with convenience.
You want a flat floor at any time but with 16" and bigger tile it becomes really important. Hardi may be the best at eating up some of the washboard uneveness but they all follow tghe floor so a slope to one wall will still there. Self Leveling Cement, with the required primer, will bring slightly sloped floors back closer to level and flat, it should be used under the mats and over the Hardibacker.
Hope that helps.