The electronic structure of a LaNiO3 bilayer grown along the [111] direction and confined between insulating layers of LaAlO3 is theoretically investigated using a combination of first-principles calculations and effective multiorbital lattice models. The local density approximation (LDA) band structure is well reproduced by a tight-binding model for the Ni eg orbitals defined on the buckled honeycomb lattice. We highlight peculiar properties of this model, which include almost flat bands as well as linear and quadratic band-crossing points. The effect of local correlations is discussed within the LDA+U scheme and within the Hartree-Fock approximation for interacting multiorbital lattice models. Over a wide range of interaction parameters, we find that a ferromagnetic phase is energetically favored. We discuss the possibility of additional orbital order, which could stabilize a spontaneous Chern insulator with chiral edge modes or a staggered orbital phase with a √3×√3 reconstruction of the unit cell. By studying an interacting nickel-oxygen lattice model, we find that the stability of these orbitally ordered phases also depends on the value of the charge-transfer energy. Controlling the charge-transfer energy might therefore be an important step towards engineering exotic electronic phases in certain classes of oxide heterostructures.