Galactic core-collapse Supernovae could be powerful sources of Gravitational Waves~(GWs) induced by hydrodynamical instabilities and highly-time dependent anisotropic emission of neutrinos. In this work, we analyze the expected gravitational wave signals from two reference SN models started from 3D progenitors and evolved continuously in 3D up to late times after the core bounce ($t_{\rm pb}>1.5\,\mathrm{s}$) by employing the PROMETHEUS-VERTEX neutrino transport code. For each considered SN model we point out how different features recognizable in GW signatures can be related to peculiar physical phenomena characterizing SN events, such as post shock-shock convection, standing accretion shock instabilities and anisotropic shock expansion. Finally, we discuss prospects of detection for current and future GW interferometers, highlighting that GW signatures from the next Galactic Supernova event can be reasonably considered in the reach of next-generation experiments working in the frequency range $f\sim1-2000\,\mathrm{Hz}$.