The origins of life likely required the cooperation among a set of molecular species interacting in a network. If so, then the earliest modes of evolutionary change would have been governed by the manners and mechanisms by which networks change their compositions over time. For molecular events, especially those in a pre-biological setting, these mechanisms have rarely been considered. We are only recently learning to apply the results of mathematical analyses of network dynamics to prebiotic events. Here, we attempt to forge connections between such analyses and the current state of knowledge in prebiotic chemistry. Of the many possible influences that could direct primordial network, six parameters emerge as the most influential when one considers the molecular characteristics of the best candidates for the emergence of biological information: polypeptides, RNA-like polymers, and lipids. These parameters are viable cores, connectivity kinetics, information control, scalability, resource availability, and compartmentalization. These parameters, both individually and jointly, guide the aggregate evolution of collectively autocatalytic sets. We are now in a position to translate these conclusions into a laboratory setting and test empirically the dynamics of prebiotic network evolution.