Employing first-principles density functional theory calculations and Wannierization of the low-energy band structure, we analyze the electronic structure of undoped, infinite-layer nickelate compounds NdNiO2, PrNiO2, and LaNiO2. Our study reveals the important role of the nonzero f -ness of Nd and Pr atoms, as opposed to the f(0) occupancy of La. The nonzero f-ness becomes effective in lowering the energy of the rare-earth 5d hybridized axial orbital, thereby enhancing the electron pockets and influencing the Fermi surface topology. The Fermi surface topology of NdNiO2 and PrNiO2 is strikingly similar, while differences are observed for LaNiO2. This difference shows up in computed doping-dependent superconducting properties of the three compounds within a weak coupling theory, which finds two-gap superconductivity for NdNiO2 and PrNiO2, and the possibility of a single-gap superconductivity for LaNiO2 with the strength of superconductivity suppressed by almost a factor of 2, compared to the Nd or Pr compound.