A mesh dependency study would prove useful for the different models in consideration. One way to do this would be validating your coefficients (lift/drag/moment) against the experimental values/data available. The right mesh resolution for the respective model would be the one matching your simulation results with the experimental results. Cheers!
I have read about the index of Resolution Quality required for LES. And it was pointed out before that a good LES is that which tends to DNS as the grid Resolution tends to the smallest scale i.e Kolmogorov scales. Therefore there is no such things as grid-Independent LES in theory, because a grid-Independent LES is essentially DNS. And therefore, the philosophy of LES loses it's meaning if it is grid Independent.
(the Advantage of LES over DNS being that LES is much more economical while it only requires the Resolution of the most energetic Eddies that determine the essential flow properties)
From what I understand with LES method, mesh size has to be in the inertial zone so it's smaller than large scale phenomena and bigger than smaller scales that would be filtered be the model. In this region energy is still transferred from larger to smaller scales.
The other answers are really complete so I will just add that there is a report collecting experimental/DNS results to validate your model characteristics on canonical cases.This is especially useful if you don't really know the performance of your LES code. It is also useful to understand the differences between your SGS models, which will have an influence on the mesh size you choose.
The LES method pretends to use less resolution than DNS solvings. Then LES has a multiple of Kolmogorov scale \eta_k inside. You decide how coarse is this reduction of meshing in order to cut-off the cascade spectrum of turbulent kinetic energy vs. wave number. In the domain you are working of, locate the points where the kolmogorov scale is the lower and the higher. This will configures the adequate refinement, thus you will have the same order of kolmogorov scales inside each mesh unit.