Using updated and improved atomistic models for the polymorphs of calcium carbonate and their constituent ions in solution, we revisit the question of surface energetics and nanoparticle stability. Using a simple lattice-based Monte Carlo scheme, we generate nanoparticle configurations in vacuum for all three biologically relevant polymorphs of calcium carbonate and establish that the bulk energetic ordering of polymorphs persists to the nanoscale. In aqueous environments, results based on surface enthalpy alone indicate that formation of mineral water interfaces is marginally favorable in many cases. Including an estimate of lost entropy due to formation of structured water layers is sufficient to reverse this observation, implying a delicate balance of enthalpy and entropy at crystalline CaCO3. In contradiction to some previous studies, we find that small calcite nanoparticles with diameters in the range of 1.8-4.1 nm do not retain an ordered structure on nanosecond time scales. The consequences of these results for simulation studies of biomineralization are discussed.