Insulate all six surfaces, meaning four walls, ceiling and floor, even if your cellar rests on solid earth. The cold-room contractor who advises that it is not necessary to insulate the floor because it rests on solid earth does not know what he is talking about and should be avoided. Heat absorbed by the ground during the day goes through the earth and rises through the floor. Additionally, cold goes through the floor, spreads through the earth, and could cause condensation on adjoining house walls. If your cellar is on an upper floor, insulation of the floor is mandatory to avoid condensation on the ceiling of the room below, which if it is your neighbour's could lead to very unpleasant relations especially if his ceiling plaster gives way.
Similar considerations apply to insulation of the ceiling in cellars built within apartments.
Domestic apartments are not built to take very heavy loads. A case of wine weighs 18-20 kg. Whether it is you or your neighbour below, structural cracks are not desirable. It is better to provide over rather than under-capacity of cooling because it imposes less strain on the compressor. And insist on high-quality equipment, especially the controlling thermostat.