A recently developed force field for interactions of water molecules with the (110) surface of rutile (alpha-TiO2) has been generalized for atomistically detailed molecular dynamics simulations of the interfacial structure of the uncharged mineral surface in contact with liquid SPC/E water at 298 K and 1 atm and for negatively charged surfaces in contact with SPC/E water containing dissolved electrolyte ions (Rb+, Sr2+, Zn2+, Na+, Ca2+, Cl-). Both hydroxylated (dissociative) and nonhydroxylated (associative) surfaces are simulated, since both types of water-surface interactions have been postulated from ab initio calculations and spectroscopic studies under near-vacuum conditions. The positions of water molecules at the interface were found to be very similar for both hydroxylated and nonhydroxylated surfaces, with either terminal hydroxyl groups or associated water molecules occupying the site above each terminal titanium atom. Beyond these surface oxygens, a single additional layer of adsorbed water molecules occupies distinct sites related to the underlying crystal surface structure. The water structure and mobility quickly decay to the bulk liquid properties beyond this second layer. The hydrogen-bonding structure and water orientation in these first two oxygen layers are somewhat sensitive to the hydroxylation of the surface, as are the electrostatic profiles. For all simulated properties, including space-dependent diffusivity of water molecules, the influence of the interface is negligible beyond distances of about 15 Angstrom from the surface. Increasing the temperature to 448 K while maintaining the density at the liquid-vapor saturated condition had minimal effect on the interfacial structure and electrostatic properties. These results are foundational to the simulation of dissolved ion interactions with the surface and the comparison of the simulation results with X-ray standing wave and crystal truncation rod measurements of water and electrolyte solutions in contact with rutile (110) single-crystal surfaces presented in Part 2 of this series.