Within a supersymmetric (SUSY) type-I seesaw framework with flavor-blind universal boundary conditions, we study the consequences of requiring that the observed baryon asymmetry of the Universe be explained by either thermal or non-thermal leptogenesis. In the former case, we find that the parameter space is very constrained. In the bulk and stop-coannihilation regions of mSUGRA parameter space (that are consistent with the measured dark matter abundance), lepton flavor-violating (LFV) processes are accessible at MEG and future experiments. However, the very high reheat temperature of the Universe needed after inflation (of about 10^{12} GeV) leads to a severe gravitino problem, which disfavors either thermal leptogenesis or neutralino dark matter. Non-thermal leptogenesis in the preheating phase from SUSY flat directions relaxes the gravitino problem by lowering the required reheat temperature. The baryon asymmetry can then be explained while preserving neutralino dark matter, and for the bulk or stop-coannihilation regions LFV processes should be observed in current or future experiments.