Altho there are "isolation" mats used under some tile installation processes, usually large units like slate, or marble, linolium will probably cause you nothing but trouble.
Remove the linolium and prep the subsurface like you know you should. You may also need to provide a good underlayment, like 1/4" cement board, if your existing subfloor is not sufficient. Make note that the new tile floor will change the "thickness" of your floor and dependening on your tile, you may have to adjust a few appliances such as the dish washer. Don't freak out, this is not a big deal, altho you may have to have this job done if you are not into small construction projects.
You probably do not have an issue with the structure to hold up your new flooring, but think this thru,also. If it is a "large" area, you may have to double up a few floor joists to hold it up and "stiffen" things so as to remove any "bounce" in the floor that would crack your tile or grout.
Altho I like tile, have Mexican Saltios in my home, you can buy some really good vinyl flooring that looks great. In fact, I am old enough to really like the old linolium floors with the patterns from the '50's. They go with anything and look great. Again, depends on your situation.