Clustering of water molecules on charged particles has been studied using the method of molecular dynamics simulations. A selected set of model metal and halogen ions, carrying both positive and negative charges, is chosen as nucleation centers for water molecules. The influence of the ion charge, its size, and short-range interactions on the local structure, and kinetic characteristics are investigated for the ion-centered clusters of 20 and 30 water molecules at 200 and 300 K, respectively. It is shown, based on radial densities, energy, polarization profiles, and orientational distribution functions, that the local water structure in the clusters becomes perturbed to a larger degree around negative ions compared to ions carrying a corresponding positive charge. The electric field of an anion is more effectively screened by the first hydration shell, resulting in a weaker dependence of the relaxation processes on the ion field in the second hydration shell. The dependence of the work of cluster formation on the ion radius is more pronounced in the case of negative ions. The dependence of the properties on the cluster size are investigated. It was found that for the water-alkali ion system potentials used, the dependence of the work of cluster formation on the number of water molecules has a minimum at about N = 30. The obtained work of cluster formation for the anions was found to be consistently less than that for the cations. Unfortunately, this work of formation does not alone provide an answer to the still unsolved problem of sign preference connected to water condensation on charged particles in atmospheric conditions.