The electronic and vibrational properties of TiS2, ZrS2, and HfS2 have been studied using dispersion-corrected hybrid density functional methods. The periodic trends in electronic band structures, electronic transport coefficients, IR and Raman spectra, and phonon dispersion relations were investigated. Comparison to the available experimental data shows that the applied DFT methodology is suitable for the investigation of the layered transition metal dichalcogenide materials with weak interlayer van der Waals interactions. The choice of damping function in the D3 dispersion correction proved to have a surprisingly large effect. Systematic investigation of the periodic trends within group 4 disulfides reveals that TiS2 shows many differences to ZrS2 and HfS2 due to the more covalent M-S bonding in TiS2. ZrS2 and HfS2 mainly show differences for properties where the atomic mass plays a role. All three compounds show similar Seebeck coefficients but clear differences in the relative electrical conductivity of cross- and in-plane directions. The transport and vibrational properties of thin TiS2 single crystals were also investigated experimentally.