By employing first-principles electronic structure calculations we investigate nickelate superlattices [LaNiO3](1)/ [LaAlO3](1) and [LaNiO3](1)/[SrTiO3](1) with (001) orientation under epitaxial tensile strain. Within density functional theory augmented by mean-field treatment of on-site electronic correlations, the ground states show remarkable dependence on the correlation strength and the strain. In the weakly and intermediately correlated regimes with small epitaxial strain, the charge-disproportionated insulating states with antiferromagneitc order is favored over the other orbital and spin ordered phases. On the other hand, in the strongly correlated regime or under the large tensile strain, ferromagnetic spin states with Jahn-Teller orbital order become most stable. The effect from polar interfaces in LaNiO3](1)/[SrTiO3](1) is found to be noticeable in our single-layered geometry. Detailed discussion is presented in comparison with previous experimental and theoretical studies.