We use ab initio molecular dynamics simulations to study the effect of ions on the structure and dynamics of the quartz(101) water interface. We study several IA (Na+, Rb+) and IIA (Mg2+, Sr2+) cations, with Cl- as counterion, adsorbed onto acidic, neutral, and basic surface configurations at 300 and 373 K. We find that both cations and anions can bond directly to the surface and perturb the local H-bond network. The adsorbed ions promote the formation of intrasurface H-bonds, as shown by vibrational density of states and orientations of the surface silanols. Both local and global structural correlations of the interfacial H-bond network are studied using a structural definition of the H-bond and a network correlation function. We find the ions' effect on the solvent structure exhibits a complex dependence on specific surface interactions. The structure-making properties of ions are enhanced at the quartz surface, particularly for ions adsorbed without a complete hydration shell, and the structuring effect extends beyond the first solvation shell. The ions have a lesser effect on solvent structure in solution, especially in the presence of counterions. In fact, cations that are the greatest "structure makers" at the surface are the greatest "structure breakers" when in solution with a counterion. Therefore, we find the ions cannot be simply classified as "structure making" or "structure breaking". We discuss the implications of these findings for the effect of ions on the dissolution rate, surface charge, and solvent structure.