Do you have a real good reason for installing ceramic tile on the floor? We have occasion to use our bathrooms while barefoot, and I would think if you do the same, you'll find ceramic tile to be quite cold-feeling on the bottoms of your feet.
A few months ago I refloored our half bath. It had a very old, glued linoleum that was a devil to tear off, similar to yours. Came up in bits and pieces. Bought a remnant of "flexifloor" vinyl at Jerry's Home Improvement, big enough for the half bath and the rear entry hall, for $70. Used Duroc (water putty) to level out the dips and doodles, let it set a day, then scuffed (sanded) the lumps off and put down the vinyl. Neat stuff, no glue needed, just held down by the floor moldings along the walls, and the toilet, of course. Looks great, feels warm and seems to wear like iron, although time will tell.