For relaxation of transition metal dichalcogenides (e.g.: WS2) using the VASP code, what is the best choice for vdW correction method (e.g.: DFT-D2, DFT-D3 or optB88-vdW) that can give you good results ?
DFT-D2 is simple and reliable. I've used DFT-D2 for most of my worked on 2D materials but I do I have to caution you that I have not specifically work on TMGs. You can test out the results you obtain from both DFT-D2 and DFT-D3 and compare them. Another idea is to look at literature. There is a labyrinth of data on TMGs and you can look under the 'methods' section of the papers.
This also depends on the kind of functional you use in KS-DFT. If you're using LDA, it's not practical to use vdw corrections because LDA already over-binds and using a vdw correction makes it only worse. If you're using PBE for example, it should be fine.