MoS2 is a promising low-cost catalyst for the hydrogen evolution reaction (HER). In order to enhance the HER activity of the inert basal plane, we perform an extensive density functional theory screening (DFT) of substitutional doping. Substituted basal planes may have many more active sites per MoS2 formula unit compared to the active sites located on the edges. We assess the electrocatalytic activity by explicitly considering the electrochemical potential via grand canonical DFT in combination with the linearized Poisson-Boltzmann equation. We screen 17 abundant elements for molybdenum doping and 5 elements for sulfur substitution. For the first time in such a screening study, we investigate not only the adsorption of H, but also of OH and H2O to explore the solvent effect, since the reaction takes place in an aqueous medium. Two other phenomena that could hinder hydrogen production at these sites are investigated, namely H2S release and the (local) segregation/dispersion tendency of the dopants in the basal surface. Compared to the pristine MoS2 nanosheets, our results show that most of the dopants significantly enhance the electrocatalytic activity. Considering all the evaluated factors, we identify the most promising systems: Dimers of Ti, Zr, and Hf, and the substitution of S by P are predicted to lead to stable active sites at the basal level with overpotentials of about 0.2 V.