With the goal to improve their photostability, InP-based QDs are passivated with three types of inorganic shells, namely (i) a gradient ZnSe$_x$S$_{1-x}$ shell, (ii) an additional ZnS shell on top of the gradient shell with two different thicknesses (core/shell/shell, CSS), (iii) an alumina coating on top of ZnS. All three systems have photoluminescence quantum yields (PLQY) > 50% and similar PL decay times (64-67 ns). To assess their photostability they are incorporated into a transparent poly (methyl methacrylate) (PMMA) matrix and exposed to continuous irradiation with simulated sunlight in a climate chamber. The alumina coated core/shell system exhibits the highest stability in terms of PLQY retention as well as the lowest shift of the PL maximum and lowest increase of the PL linewidth, followed by the CSS QDs and finally the gradient shell system. By means of XPS studies we identify the degradation of the ZnS outer layer and concomitant oxidation of the emissive InZnP core as the main origins of degradation in the gradient structure. These modifications do not occur in the case of the alumina-capped sample, which exhibits excellent chemical stability. The gradient shell and CSS systems could be transferred to the aqueous phase using surface ligand exchange with penicillamine. Cytotoxicity studies on human primary keratinocytes revealed that exposure for 24 h to 6.25-100 nM of QDs did not affect cell viability. However, a trend toward reduced cell proliferation is observed for higher concentrations of gradient shell and CSS QDs with a thin ZnS shell, while CSS QDs with a thicker ZnS shell do not exhibit any impact.