Perovskite oxides have a characteristic ABO₃ structure that is able to accommodate a large number of different cations in the A and B locations. In particular, perovskites with Mo on the B site, including SrMoO₃ and PbMoO₃ have recently been fabricated. SrMoO₃ has been shown to have high electron mobility, and PbMoO₃ exhibits metallic behavior to low temperatures with a resistivity displaying a sublinear dependence on temperature. We use first-principles calculations based on density-functional theory (DFT) plus Hubbard U to investigate the family of perovskite molybdenates: SrMoO₃, PbMoO₃, and LaMoO₃ in order to determine their ground-state atomic and magnetic structures. We determine the dependence with the choice of U, exchange-correlation functional, and implementation with respect to DFT code. Finally, we interpret the ground-state structures in terms of unstable phonons of higher symmetry structures including cubic Pm-3m.