It seems like I should replace the floor first.
Is that true?
My house was built on a slab, and I know there are two layers of linoleum, and maybe asbestos, all over concrete.
I would appreciate any advice.
Yes, a gut remodel should have everything in the room removed back to the studs (for ease and cheaper running of the needed new wiring and plumbing) and then you rebuild everything from the inside out, and the bottom up.