Photovoltaic (PV) devices play a key role in solar-to-electricity energy conversion at small and large scales; unfortunately, their efficiency heavily depends on optimal weather and environmental conditions. The optimal scenario would be to extend the capabilities of PV devices so that they are also able to harvest energy from environmental sources other than light. An optimal solution is represented by hybrid photovoltaic-triboelectric (PV-TENG) devices which have both photovoltaic and triboelectric capabilities for electric power generation. Two-dimensional transition metal dichalcogenides (TMDs) are highly promising candidates for such PV-TENG devices, thanks to the easy tunability of their electrical, optical, mechanical, and chemical properties. In this respect, we here propose a quantum mechanical study to identify suitable TMD-based chemical compositions with optimal photovoltaic and triboelectric generation properties. Among the considered materials, we identify MoTe2/WS2, MoS2/WSe2, WS2/TiO2, WS2/IrO2, and MoS2/WTe2 as the most promising bilayer compositions; under operative conditions, the band gap varies in the range 0.51-1.61 eV, ensuring the photovoltaic activity, while the relative motion of the layers may produce an electromotive force between 1.21 and 3.21 V (triboelectric generation) with a TMD/TMD interface area equal to about 200 Å2. The results constitute theoretical guidelines on how to check if specific chemical compositions of TMD bilayers are optimal for a combined photovoltaic and triboelectric power generation. Thanks to its generality, the presented approach can be promptly extended to van der Waals heterostructures other than those here considered and implemented in automated workflows for the search of novel low-dimensional materials with target PV and TENG response.