The Hartree-Fock-Popov theory of interacting Bose particles is developed, for modeling exciton-polaritons in semiconductor microcavities undergoing Bose-Einstein condensation. A self-consistent treatment of the linear exciton-photon coupling and of the exciton nonlinearity provides a thermal equilibrium description of the collective excitation spectrum, of the polariton energy shifts and of the phase diagram. Quantitative predictions support recent experimental findings.