Actually you want to try to prevent your floor from moving. Let's say you use mastic and the tile does move without popping the tiles out- the grout still will crack and possibly pop out.
Use a latex modified thinset with a 3/8" mortar bed. This will give your floor added strength and stability with just enough flex to account for extreme stress. Also use a latex grout or add an acrylic latex additive to your standard grout to give it the same properties as well as offer some protection from staining.