Since the discovery of their excellent performance as the light-absorbing semiconducting component in photovoltaic cells, the PbX3CH3NH3 (X = I, Br, Cl) perovskites have received renewed attention. The five polymorphs stable above 200 K - the tetragonal phases for X = I, Br, Cl and the cubic phases for X = I, Br - were studied using periodic DFT calculations involving hybrid functionals (PBE0 and HSE), employing Gaussian-type orbitals as well as plane waves and including relativistic effects (spin-orbit coupling). The influence of the halogen substitution and of the crystal phase on these properties is analysed by comparing the properties obtained in this study to the experimental ones and to the theoretical ones computed using other methods. We show that an accurate treatment of these systems requires the description of dispersion forces and spin-orbit coupling. The different time scales for the electronic and vibrational components of the polarizability inspire the hypothesis that several interfacial charge transfer mechanisms are encountered in the working principle of the photovoltaic devices involving these perovskite materials. The heavy elements in the structure (Pb, I) play a major role in the high polarizability and the low effective charge carrier masses and hence in the low exciton binding energies and the high charge mobility. This systematic work on the PbX3CH3NH3 family offers to theoreticians an overview of the landscape of quantum chemical methods to enable a reasonable choice of methodology for studying these systems.