The electronic phase diagram has been studied in half-doped manganese perovskite oxides (RE0.5AE0.5)MnO3 (where RE is a rare-earth trivalent ion and AE is a divalent alkaline-earth ion). The electronic ground state is found to depend strongly on the ionic radii of (RE0.5AE0.5) sites and on the ordering of RE and AE ions. We have also investigated the oxygen-isotope effect on the phase diagram of the (RE0.5AE0.5)-site disordered structure. It is found that the oxygen-isotope exponent decreases systematically with increasing the ionic radii of the (RE0.5AE0.5) sites. Our data suggest that the polaronic effect and random potential play important roles in competition of various ground states. Our results also provide evidence that polarons play a crucial role in the phenomena of colossal magnetoresistance.