We propose a pair-condensate variational approach (PCV) to determine a set of the most important collective pairs in the description of low-lying states in atomic nuclei. Having available the precise details on these key collective pairs -- their spin, parity, and structure -- can be particularly useful in calculations based on the nucleon-pair approximation (NPA), helping to reduce their uncertainties. In trial calculations for the transitional Ba isotopes, our variational approach describes the evolution of quadrupole-deformation properties similar to Hartree-Fock treatments, while at the same time highlighting the $γ$ softness of $^{132}$Ba. Our approach can conclusively determine which collective pairs are critical for obtaining the lowest possible yrast, quasi-beta, quasi-gamma bands, producing both the level structure of these bands and related B(E2) values in reasonable consistency with experiment. These trial calculations suggest that with our PCV approach the NPA can be meaningfully applied to transitional nuclei with a wide spectrum of shapes. We also show that while neutron negative-parity pairs could in principle have an important impact on backbending in $^{132}$Ba, they are not favored for this nucleus.

16 pages, 6 figures