Linoleum/Vinyl Sheet Flooring

While you CAN also tile over the existing floor as long as it's stuck down well and not lifting anywhere, it's not really recommended that you do that. The reason why is that the life of your new tile floor will be limited to the remaining life in your existing floor's glue. Once that old glue starts to let go, that's the end of your new tiling.

Mapei is probably the biggest name in flooring cements in the world and last I checked, Homeless Depot was selling Mapei products. Mapei makes a cement based floor leveling compound called "Planipatch" which is sold by the bag. They also make an "additive" (pronounced "adhesive") called "Planipatch Plus", which is really nothing more than a latex glue. On existing linoleum, you mix the Planipatch powder with the Planipatch Plus additive only so that the slurry you mix up sticks like he11. You then scrape off any high spots with a sharp paint scraper, vaccuum up, and apply a second coat. This time, dilute the Planipatch Plus with 3 parts water and use that solution to mix up your slurry, and spread that over the first coat. You then scrape or sand down any high spots in that second coat and vaccuum up. Finally, if a third coat is needed to get the floor smooth, you mix up that third coat using Planipatch mixed with water only. The resulting coat will be soft enough to sand smooth easily. Always use a bright light laying on the floor to help you identify high spots and any low spots that need to be filled with more floor patch. The above is called "floating" the floor to prepare it for a new flooring material.

And, if it wuz me, I would caulk between the new flooring and your toilet floor flange to ensure that if you ever have a leaking wax ring, the water shows up on top of your floor well before it shows up on any ceiling below. That will give you time to replace the leaking wax ring before you have to replace water damaged drywall or plaster.