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If I were to do it, I'd want to reinforce the floor with cement-fibre boards before putting anything else on it. If the floor is squeaky, it might not be stiff enough for ceramic tiles, even if you put more screws into it. Haven't tried Schluter Ditra myself, but the principle is sound. If you want a floating/decoupled floor, it's probably the simplest alternative. Other methods include either using thick layers of mortar and sand, or plastics sheets and leveling compound.

EDIT: By the way, I'd remove the linoleum as well. Not only isn't it a good supstrate for anything, if it's been there long enough, mold growth isn't unusual. This is especially true under dishwashers and refridgerators.