Sub flooring requirements for 2 X 1 rectangle tile
Wow sure that floor would bounce. Rip up the old tile and use plywood decking. I can’t remember if you can get 3/4 in t&amp;g but know you can get 1”. Since the strips are not t&amp;g I would want to go thicker if possible. If not use a lot of construction adhesive and screw the plywood down.  

Next step is your backer board. (I usually put thinset or mastic under my backer and screw it down.) The more solid your base is the better chance of a long life you have (for your tile). After that you are ready to tile. 

The threshold will be angled but that is the only way to do it right. I have dropped a finishing hammer from the ceiling on a 4” tile.  I was sure I bullseyed the tile but it was ok. I got lucky but part of that luck came from the base the tile was on. I have repaired tile that a heavy cooking spoon fell from the counter and cracked the tile--it did not have a good base. 

Don’t skimp, you should not have an observable flex in the flooring if you want it to last.