Taking up the comode is much much easier to lay tile than to work around the curves of the comode base. But you have to know how to remove it and to reinstall it. be sure upon re installing to put in a new wax ring and to remove all the old ring.
YOu may have to get a pipe extension fitting since your raising the comode up 1/4 inch. Be ready to ask for this. Next, make sure that you tighten up the floor porcelin bolts very easy. Run them down by hand, sit on the comode and waller a bit, then tighten down again, sit again and waller and tighten again. The wallering compresses the ring and sets the fitting and its important. Do not just run the bolts down and think that that is it.
Jay, the next question is how is the quality of the sub flooring? If it is nice and smooth and in good shape, I would tile over this after I float out the floor, with a good levelor.
I would not use a cementious board as that will raise your comode even more, this board is 1/2 inch I believe. So combined that would be 3/4 inch.
The vanity again, I would shim it up or carefull pry it up and lay a course of tile under this base also. You do not have to go all the way, just one tile layer only.
Now another issue is where to start. I like to lay out a dry floor to see just how things will come in and to minimize cutting.
I like to start at the tub with full tiles and work to the door and hide the over lap tiles under the threshold to the carpeted hall way, if one in your case.
Then I like to start on the wall you see when you sit on the comode with a complete tile then work to the back of the comode area with cut tile.
Make sure that you use water proof mastic and apply it to specifications on box. Also, allow the mastic to dry for two days before applying grout, then allow the grout to dry for three days before sealing the grout lines with pure silicon.
Its fun and exciting, be sure to always factor in a 5% breakage factor when buying tile. This will save you and it works. By 5% more than you need.