In a previously presented proof-of-principle study we established a parametrized spherically symmetric explosion method (PUSH) that can reproduce many features of core-collapse supernovae. The present paper goes beyond a specific application that is able to reproduce observational properties of SN1987A and performs a systematic study of the explosion properties for an extensive set of non-rotating, solar metallicity stellar progenitor models in the mass range from 10.8 to 120 M$_odot$.This includes the transition from neutron stars to black holes as the final result of the collapse of massive stars, and the relation of the latter to supernovae and faint/failed supernovae. The present paper provides the basis for extended nucleosynthesis predictions in a forthcoming paper to be employed in galactic evolution models.