You have no general recipe, as the accuracy of the different DFT-D schemes depend on the nature of the system (but, also on the system size and topology) and the DFT calculation scheme (especially the exchange correlation functionals). Ideally, someone has to do a high level electronic correlation HFT calculation (at least MP2) for the system of interest (or fragments of it) and use the results to calibrate your DFT-D scheme (dispersion calculation method, parameters).
Generally f you want to use Grimme correction, you should remember that you include dispersion energy as an add-on, so if a functional is aimed at recovering dispersion energy itself, like M06-2X, addition of Grimme correction leads to double counting of dispersion energy. I think the article may be helpful for your purposes.
"Generally f you want to use Grimme correction, you should remember that you include dispersion energy as an add-on, so if a functional is aimed at recovering dispersion energy itself, like M06-2X, addition of Grimme correction leads to double counting of dispersion energy."
It is true, and yet e.g. M06-D3 gives better results (in terms of mean average error) than M06 for the S22 set. So while conceptually it makes little sense, from the results point of view it may be very well justified.