Transition-metal dichalcogenides (TMDs) are valuable as solid lubricants because of their layered structure, which allows for easy shearing along the basal planes. Using Density Functional Theory (DFT), we conducted a first-principles study of the sliding properties of several TMD bilayers: MoS2, MoTe2, WS2, WSe2, VS2, VSe2, TaS2, TaSe2, TiS2, TiSe2, HfS2, ZrS2, MoS2WS2, and MoS2VS2. Given the crucial role of van der Waals (vdW) interactions in accurately describing the interlayer interactions in TMD bilayers, we employed vdW-corrected DFT functionals. Our research confirms the dominance of vdW effects by estimating the fraction of interlayer binding energy attributable to these interactions. We also examined how the choice of different vdW-corrected DFT functionals might influence quantitative results. Using MoS2 as a reference TMD bilayer system, we found that most other TMD bilayers studied exhibit stronger interlayer bonds and greater corrugation. However, TiSe2 shows a profile similar to MoS2, while, interestingly, TiS2, VS2, and ZrS2 are characterized by weaker bonding and lower corrugation than MoS2. We explored relationships between various properties of TMD bilayers, with a particular focus on potential connections between tribological and electronic properties often characteristic of solid interfaces. To this end, we evaluated adhesion energies, work of separation, charge density redistributions in interface regions, differential charge densities, and corrugation. While corrugation and, therefore, resistance to sliding generally tend to increase with the size of the chalcogen element and are typically proportional to the adhesion energy, the relationships between other structural, energetic, and electronic properties do not follow a single, well-defined trend.