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Motivated by the recently reported high-temperature superconductivity in the bilayer La₃Ni₂O₇ (LNO) under pressure, we comprehensively study this system. The Ni 3z²−r² orbitals form a bonding-antibonding molecular orbital state via the O p_z inducing a “dimer” lattice in the LNO bilayers ^[1]. The Fermi surface consists of two sheets with mixed e_g orbitals, and a hole pocket defined by the 3z²−r² orbital, suggesting a Ni two-orbital minimum model<span style="font-size:10.8333px">. At low pressures, the Amam phase is stable, containing the Y²⁻ mode distortion from the Fmmm phase, while the Fmmm phase is unstable phase. Because of small differences in enthalpy and a considerable Y²⁻ mode amplitude, the two phases may coexist between 10.6 and 14 Gpa, beyond which the Fmmm phase dominates ^[2]. In addition, we found that the magnetic stripe-type spin order with wavevector (π, 0) becomes stable at intermediate Hubbard and Hund couplings, caused by the competition between the intraorbital AFM and interorbital FM tendencies ^[1,3]. Pairing is induced in the s±-wave channel due to nesting between the M= (π, π) centered pockets and portions of the Fermi surface centered at X= (π, 0) and Y= (0, π) points. By replacement of rare-earth (RE) elements, six candidates were found to become stable in the Fmmm phase at the pressure range we studied. Similar to the case of LNO, the s±-wave pairing tendency dominates in all candidates ^[3]. Our results suggest that LNO is already the “optimal" candidate, with Ce a close competitor, among the whole RE bilayer nickelates.