The first thing you should do is plan your new floor

The first thing you should do is plan your new floor. What size tile, what will the threshold be, what goes underneath, etc? Sketch it out - sketch it again.

I would recommend removing all the fixtures before beginning demo but I had to complete this project after work so it took several weeks of on and off attention. I left the toilet and vanity hooked up to the water lines because I didn't have faith in the shutoff valves in the bathroom to hold for several weeks so they may appear in some photos. If you can, remove before demo.

To begin demo remove the trim from the walls and cut a small square of the floor up to see what is underneath and to provide a spot to begin the floor demo. Using a wonderbar/crowbar/hammer pull up hardwood.

NOTE: When you get close to the doorway - stop demo and prep the transition zone where the tile will meet the hardwood in the hallway.
Because you sketched your new floor several times you already know what the plan for the threshold is, right? Snap your chalk lines in the room from where you will start tiling. Measure from the chalk line parallel to the threshold and mark both sides of the doorway.

Snap a chalk line between the left and right door jam. Repeat if necessary to get it just right (my wife and I did it 3 times to be sure). There is no going back if you cut off too much.

Screw a straight edge (scrap lumber with good lines) into bathroom accessoriesthe floor on the BATHROOM side of the chalk line.I used the straight edge as a guide for my saw using the rounded blade to cut 75% through hardwood. I then used a straight blade to cut through the hardwood without damaging the subfloor (mark blade with tape the thickness of hardwood - e.g., 3/4 inch). Clear out hardwood from underneath door frame with drill/dremel/rotozip.
Once I removed the toilet I was able to see part of the original problem. The toilet flange was installed incorrectly as you can see the bolts were placed in two U shaped recesses in the flange and not in the proper channels for the bolts. The flange bolt "channels" should be perpendicular to the back wall so that the bolts could float while squaring the toilet in the room. Incorrect bolt placement split the flange and likely contributed to a cracked toilet.

To repair, cut a whole in the subfloor near the flange and big enough for a reciprocating saw to fit under the floor. Cut the flange pipe as near to the bottom of the subfloor as possible, this will allow the most amount of pipe to work with when installing the new flange. Once flange is cut remove the subfloor using a pry bar and hammer.

Measure new subfloor dimensions and cut replacement piece. Also measure to the center of the drain pipe from at least two sides. Measure diameter of pipebathroom faucet to trace on new subfloor. Using jig saw, cut our hole for drain pipe.

To replace toilet flange you will need a length of pipe, coupler, pvc primer, pvc glue, toilet flange. Use the couple to join the old pipe to the new pipe that the flange will connect to. Measure and cut old/new/coupler pipe so that the drain is right below the subfloor. DO NOT glue the toilet flange on until after subfloor is installed. Put liquid nail on joist and nail down new subfloor. Then prime/glue drain pipe and slide toilet flange on. When joining pipes hold together for ~30 seconds to ensure bonding. Screw in the toilet flange and then put an old t-shirt wrapped in a bag in the drain - unless you like the funk.