First-principles studies of two-dimensional transition metal dichalcogenides have contributed considerably to the understanding of their dielectric, optical, elastic, and vibrational properties. The majority of works to date focus on a single material or physical property. Here we use a single first-principles methodology on the whole family of systems to investigate in depth the relationships between different physical properties, the underlying symmetry, and the composition of these materials, and observe trends. We compare to bulk counterparts to show strong interlayer effects in triclinic compounds, and relationships between these monolayer compounds become apparent. These trends can then be exploited by the materials science, nanoscience, and chemistry communities to better design devices and heterostructures for specific functionalities.