A fundamental weakness of density functional theory (DFT) is the difficulty in making systematic improvements to approximations for the exchange and correlation functionals. In this paper, we follow a wave-function-based approach [N.I. Gidopoulos, Phys. Rev. A 83, 040502 (2011)] to develop perturbative expansions of the Kohn-Sham (KS) potential. Our method is not impeded by the problem of variational collapse of the second-order correlation energy functional. Arguing physically that a small magnitude of the correlation energy implies weak perturbation and hence fast convergence of the perturbative expansion for the interacting state and for the KS potential, we discuss several choices for the zeroth-order Hamiltonian in such expansions. Our first two choices yield KS potentials containing only Hartree and exchange terms: the exchange-only optimized effective potential (xOEP), also known as the exact-exchange potential (EXX), and the Local Fock exchange (LFX) potential. Finally, we choose the zeroth order Hamiltonian that corresponds to minimum magnitude of the second order correlation energy, aiming to obtain at first order the most accurate approximation for the KS potential with Hartree, exchange and correlation character.