with the wood up, do you see any cracks in the concrete foundation? How old is the home?
Where I am going is for you to test and decide if you want to mount the ceramic directly to the foundation or add a subflooring to attach the ceramic to so that if the concrete slab cracks the ceramic will NOT also.
If you want to go directly to the slab here is what I would do. lay down a plastic tarp over the intended area and let it sit there for one day. Then remove the tarp and test for water vapor either on the slab or under the tarp itself. If so, you need to prep to stop the migration of water to the work area.
Then if the test shows no vapor, procede to remove all the glue and residue so the floor is smooth as a babies, you know. Any bumps will mess up the ceramic floor. when completely smooth spread your thinset by the prescribed trowel knotch and then begin your ceramic lay and use your spacers as directed. you may want to rent a water tile saw for those cuts. I am assuming that the tile is larger than 4 inch square.