This paper, Part III in the Trilogy (Ballato, Cavillon, Dragic, 2018; Dragic, Cavillon, Ballato, et al., 2018a,b), provides a road map for the development of simple core/clad optical fibers whose enhanced performance-in particular, marked reductions in optical nonlinearities-is achieved materially and not through the more conventional present routes of geometrically complex fiber design. More specifically, the material properties that give rise to Brillouin, Raman and Rayleigh scattering, transverse mode instabilities (TMI), and n 2 -mediated nonlinear effects are compiled and results on a wide range of optical fibers are discussed with a focus on trends in performance with glass composition. Furthermore, optical power scaling estimations as well as binary and ternary property diagrams associated with Rayleigh scattering, the Brillouin gain coefficient (BGC) and the thermo-optic coefficient (dn/dT) are developed and employed to graphically represent general trends with composition along with compositional targets for a single intrinsically low nonlinearity, silica-based optical fiber that can achieve the power scaling goals of future high energy fiber laser applications. A foundational finding of this work is that the high-silica content optical fibers fabricated using conventional chemical vapor deposition methods will not suffice to meet the power scaling demands of future high-power and high-energy fiber lasers.