The molybdate oxides SrMoO$_3$, PbMoO$_3$, and LaMoO$_3$ are a class of metallic perovskites that exhibit interesting properties including high mobility, and unusual resistivity behavior. We use first-principles methods based on density functional theory to explore the electronic, crystal, and magnetic structure of these materials. In order to account for the electron correlations in the partially-filled Mo $4d$ shell, a local Hubbard $U$ interaction is included. The value of $U$ is estimated via the constrained random-phase approximation approach, and the dependence of the results on the choice of $U$ are explored. For all materials, GGA+$U$ predicts a metal with an orthorhombic, antiferromagnetic structure. For LaMoO$_3$, the $Pnma$ space group is the most stable, while for SrMoO$_3$ and PbMoO$_3$, the $Imma$ and $Pnma$ structures are close in energy. The $R_4^+$ octahedral rotations for SrMoO$_3$ and PbMoO$_3$ are found to be overestimated compared to the experimental low-temperature structure.
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