We present the results of a comparative ab initio study of the atomic and electronic structure of MgO, CaO, SrO, and BaO and their relaxed (001) surfaces. Based on density functional theory, we use self-interaction-corrected pseudopotentials, which permit a reliable description of electronic properties, in particular. For the bulk crystals, we arrive at well established structural data and obtain valence as well as conduction bands, which are in very good agreement with the results of quasiparticle calculations and experiment. The calculated geometric structure of the relaxed (001) surfaces is consistent with literature data. Concerning electronic properties, the calculations reveal that MgO(001), CaO(001), and SrO(001) exhibit negative electron affinity allowing for the formation of image-potential states while BaO(001) does not. As a consequence, not only bound states, which are localized at the surface, occur in the former three cases but also a salient band of image states residing in vacuum in front of the surface appears in sections of the surface Brillouin zone. Such an image state band does not arise at the BaO(001) surface. Our results are in satisfying agreement with literature data from GW quasiparticle calculations and electron energy loss spectroscopy measurements, which are only available for MgO(001), to date.