In this work the influence of geometry and composition on the charge-induced plasmonic shifts (CIPS) of gold nanoparticles are systematically studied using Mie scattering theory and the discrete dipole approximation. The sensitivity of nanorods and nanodisks with different aspect ratio and nanoshells with different volume fractions and compositions are studied using different charging levels. The electrodynamics calculations were performed by changing the internal electron density in the Drude model for the dielectric constant of gold. We show that, for a constant volume, nanodisks and nanorods exhibit CIPS with a linear dependence on aspect ratio. Geometries having higher aspect ratio show larger CIPS. In nanoshells, increasing the volume fraction of the core causes a slow increase of CIPS at first followed by a rapid increase for larger volume fractions. In addition, we find that nanoshells with the same volume fractions exhibit larger shifts when the refractive index of the cores is larger. Furthermore, the electrodynamics results are interpreted using analytical approximations based on quasistatic theory. The qualitative understanding of geometric and composition effects on the CIPS of gold nanoparticles obtained in this work can hopefully be used to realize highly tunable charge-based active plasmonic devices.