The contact resistance of the transition metal dichalcogenide (TMD) devices is not comparable to that of their silicon counterparts, probably due to a lack of clarity in their interface chemistry. Looking beyond the conventional Schottky-Mott rule, the metal chalcogen orbital overlaps, tunnel barrier, and metal-induced gap states (MIGSs) are crucial factors determining different metals' contact properties with TMDs. Exploring their properties helps TMDs' contact resistance engineering, driven mainly by their orbital overlaps and perturbing parameters. This work presents the interface chemistry of TMDs (MoS2, MoSe2, WS2, and WSe2) with different metals (Au, Cr, Ni, and Pd) in detail using density functional theory computations. Additionally, the work discusses the role of the chalcogen vacancy and interstitial defects in the metal-TMD interactions and corresponding MIGS features. The investigations reveal that Au does not show any significant MIGS due to its weak interactions with all the TMDs. However, other investigated metals have a strong affinity with TMDs, making significant MIGS contributions. All the metals offer n-type doping characteristics to TMDs due to valence charge transfer from the metals toward TMDs. The chalcogen vacancy boosts the orbital overlaps of the TMDs with all the metals. The vacancy reduces metal-TMD interfacial distance, which can be a promising technique to reduce the tunnel barrier and contact resistance. The MIGS and defect-induced gap states (DIGSs) reflect the possibility of Fermi-level pinning in the TMDs' contacts with Cr, Ni, and Pd. Besides, the work discloses that the chalcogen vacancy converts an n-type Pd-TMD interface into p-type due to reverse charge transfer after the vacancy. Chalcogen interstitial impurity also helps with contact resistance engineering for some metal-TMD systems by reducing the bond distance of the metal TMDs. Our study highlights the possibility of defect-assisted and MIGS-based contact engineering at the metal-TMD interfaces.