We have performed an exhaustive study of energetics of (H2O)(20) clusters. Our goal is to study the role that various free-energy terms play in this popular model system and see their effects on the distribution of the (H2O)(20) clusters and in the infrared spectrum at finite temperatures. In more detail, we have studied the electronic ground-state structure energy and its long-range correlation (dispersion) part, vibrational zero-point corrections, vibrational entropy, and proton configurational entropy. Our results indicate a delicate competition between the energy terms; polyhedral water clusters are destabilized by dispersion interaction, while vibrational terms (zero-point and entropic) together with proton disorder entropy favor them against compact structural motifs, such as the pentagonal edge- or face-sharing prisms. Apart from small water clusters, our results can be used to understand the influence of these energy terms in water/ice systems in general. We have also developed energy expressions as a function of both earlier proposed and novel hydrogen bond connectivity parameters for prismatic water clusters.