We present high-level ab initio potential energy curves for barium cations and dications interacting with RG atoms (RG = rare gas). These potentials are employed to derive spectroscopic parameters for the Ba(+)-RG and Ba(2+)-RG complexes, and also to derive the transport coefficients for Ba(+) and Ba(2+) moving through a bath of the rare gas. The results are compared to the limited experimental data, which generally show reasonable agreement. We identify a large change in binding energy going from Ba(+)-He and Ba(+)-Ne to Ba(+)-Ar, which is not present in Ba(2+)-RG, and show that this is due to significant dispersion interactions in Ba(+)-RG.