We characterize the Gaia-Enceladus-Sausage kinematic structure recently discovered in the Galactic halo using photometric metallicities from the SkyMapper survey, and kinematics from Gaia radial velocities measurements. By examining the metallicity distribution functions (MDFs) of stars binned in kinematic/action spaces, we find that the $\sqrt{J_R}$ vs $L_z$ space allows for the cleanest selection of Gaia-Enceladus-Sausage stars with minimal contamination from disc or halo stars formed in situ or in other past mergers... Stars with $30 \leq \sqrt{J_R} \leq 50$ (kpc km s$^{-1})^{1/2}$ and $-500 \leq L_z \leq 500$ kpc km s$^{-1}$ have a narrow MDF centered at [Fe/H] $= -1.17$ dex with a dispersion of 0.34 dex. This [Fe/H] estimate is more metal-rich than literature estimates by $0.1-0.3$ dex. Based on the MDFs, we find that selection of Gaia-Enceladus-Sausage stars in other kinematic/action spaces without additional population information leads to contaminated samples. The clean Gaia-Enceladus-Sausage sample selected according to our criteria is slightly retrograde and lies along the blue sequence of the high $V_T$ halo CMD dual sequence. Using a galaxy mass-metallicity relation derived from cosmological simulations and assuming a mean stellar age of 10 Gyr we estimate the mass of the Gaia-Enceladus-Sausage progenitor satellite to be $10^{8.85-9.85}$ M$_{\odot}$, which is consistent with literature estimates based on disc dynamic and simulations. Additional information on detailed abundances and ages would be needed for a more sophisticated selection of purely Gaia-Enceladus-Sausage stars. (read more)