The mass surface in the A similar to 100 region of the nuclear chart is extended by the measurement of the Rb98-100 isotopes with the Penning-trap mass spectrometer ISOLTRAP at ISOLDE/CERN. The mass of Rb-100 is determined for the first time. The studied nuclides mark the known low-Z frontier of the shape transition at N = 60. To describe the shape evolution towards the krypton isotopic chain, a theoretical analysis is presented in the framework of the Hartree-Fock-Bogoliubov approach. The importance of the pairing interaction for describing the extent and strength of the region of quadrupole deformation is emphasized. A later transition to large prolate deformation or, alternatively, the predominance of oblate deformation is proposed as explanation for the different behavior of the krypton isotopes. Octupole collectivity is explored as a possible mechanism for the evolution of two-neutron separation energies around N = 56.