Ring polymer molecular dynamics experiments have been carried out to examine effects derived from nuclear quantum fluctuations at ambient conditions on equilibrium and non-equilibrium dynamical characteristics of charge solvation by a popular simple, rigid, water model, SPC/E , and for a more recent, and flexible, q-TIP4P/F model, to examine the generality of conclusions. In particular, we have recorded the relaxation of the solvent energy gap following instantaneous, ±e charge jumps in an initially uncharged Lennard-Jones-like solute. In both charge cases, quantum effects are reflected in sharper decays at the initial stages of the relaxation, which produce up to a ~20% reduction in the characteristic timescales describing the solvation processes. For anionic solvation, the magnitude of polarization fluctuations controlling the extent of the water proton localization in the first solvation shell is somewhat more marked than for cations, bringing the quantum solvation process closer to the classical case. Effects on the solvation response from the explicit incorporation of flexibility in the water Hamiltonian are also examined. Predictions from linear response theories for the overall relaxation profile and for the corresponding characteristic timescales are reasonably accurate for the solvation of cations, whereas we find that they are much less satisfactory for the anionic case.