We study the solvation and electrostatic properties of bare gold (Au) nanoparticles (NPs) of $1$-$2$ nm in size in aqueous electrolyte solutions of sodium salts of various anions with large physicochemical diversity (Cl$^-$, BF$_4$$^-$, PF$_6$$^-$, Nip$^-$(nitrophenolate), 3- and 4-valent hexacyanoferrate (HCF)) using nonpolarizable, classical molecular dynamics computer simulations. We find a substantial facet selectivity in the adsorption structure and spatial distribution of the ions at the Au-NPs: while sodium and some of the anions (e.g., Cl$^-$, HCF$^{3-}$) adsorb more at the `edgy (100) and (110) facets of the NPs, where the water hydration structure is more disordered, other ions (e.g., BF$_4$$^-$, PF$_6$$^-$, Nip$^-$) prefer to adsorb strongly on the extended and rather flat (111) facets. In particular, Nip$^-$, which features an aromatic ring in its chemical structure, adsorbs strongly and perturbs the first water monolayer structure on the NP (111) facets substantially. Moreover, we calculate adsorptions, radially-resolved electrostatic potentials, as well as the far-field effective electrostatic surface charges and potentials by mapping the long-range decay of the calculated electrostatic potential distribution onto the standard Debye-Huckel form. We show how the extrapolation of these values to other ionic strengths can be performed by an analytical Adsorption-Grahame relation between effective surface charge and potential. We find for all salts negative effective surface potentials in the range from $-10$ mV for NaCl down to about $-80$ mV for NaNip, consistent with typical experimental ranges for the zeta-potential. We discuss how these values depend on the surface definition and compare them to the explicitly calculated electrostatic potentials near the NP surface, which are highly oscillatory in the $pm 0.5$ V range.
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