The last bathroom floor I did was with 1/16th inch spacers, 12 x 12 tile. I did everything I could to water proof it. It looked good for thr 2 1/2 years I saw it. But 1 1/2 years later, it looks crapey.
So to recap... You dont like central heat and air and you would prefer linoleum???? hmmmmm!!! ok den!