We present a thorough study of the effect of basis set choice and of the three-fragment counterpoise correction for the basis set superposition error on the shape of proton-exchange energy surfaces. This has been investigated by employing the correlated MP2 method and basis sets from cc-pVDZ to aug-cc-pVTZ quality. To understand the effect of the correction and the overall accuracy of the different atomic basis sets, and to discover the best-compromise basis set for large surface scans, we computed the shape difference function between corrected and uncorrected results for the HF2-, H3O2-, H5O2+, N2H5-, and N2H7+ systems. Our results show this function to strongly depend on the system, although larger corrections are consistently observed when the more basic fragments (NH2- and OH-) are involved. Suggestions on which basis set could be used for potential energy surface scans are also given.