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In the quest to understand exotic low-dimensional magnetic states, magnetic triangular lattices offer a rich playground. With this study, we model effective magnetic interactions for the monolayer structures of a range of triangular lattice materials MX₂ (M={V,Mn,Ni}, X={Cl,Br,I}). We also took the opportunity of such a larger study to benchmark two ab-initio methods used to extract effective S={3/2,5/2,1} spin models for real materials. Additionally, by means of toy model parameters based on general properties such as filling and hybridization, we shed light on the microscopic mechanism behind the different behaviors and magnetic interactions displayed by these, apparently similar, systems. In particular, the considered relatively light magnetic metal ions have small spin-orbit coupling (SOC), which allows to effectively tune the SOC by interchanging the ligand elements. We find that the corresponding SOC matrix-elements differ strongly from the atomic limit and that SOC effects manifest only in anisotropic exchange and single-ion anisotropy for specific fillings. Noticeably, for monolayer NiI₂ we do find a sizeable Kitaev coupling, suggested in previous works.