Li-S batteries are promising alternatives due to their proven increased gravimetric capacity compared to Li-ion batteries. However, their development is hindered by many technical issues, one of the most challenging being the dissolution and shuttle of polysulfide species, which causes irreversible loss of cathode material leading to rapid capacity fading. Among the possible strategies to mitigate this effect, the choice of suitable solvents is easy to implement and has large room for improvement. To guide this quest, computationally-aided optimization is a powerful tool, provided that suitable descriptors are used to screen possible solvents. In this work, molecular dynamics simulations were performed for a typical lithium polysulfide Li2S6 dissolved in different solvents. Diffusion coefficients and their related activation energies were calculated, and thermodynamic properties like solvation energies and entropies were also evaluated. Additionally, a theoretical framework for computing the relative solubilities of lithium polysulfide is provided. For the set of solvents considered, we found that the system's viscosity appears as an important descriptor to correlate with different system properties. The donor number of the solvent also appears as a valid descriptor, for low-viscosity solvents. In general, it was found that higher viscosity solvents lead to lower diffusion rates and higher polysulfide solubility. These results suggest that the optimal choice to reduce the shuttle is a trade-off between high-viscosity solvents to reduce polysulfide diffusion and low-viscosity solvents to reduce its solubility, which could be further improved by properly tuning the donor number.