The role of historical contingency in the origin of life is one of the great unknowns in modern science. Only one example of life exists—one that proceeded from a single self-replicating organism (or a set of replicating hypercycles) to the vast complexity we see today in Earth's biosphere. We know that emergent life has the potential to evolve great increases in complexity, but it is unknown if evolvability is automatic given any self-replicating organism. At the same time, it is difficult to test such questions in biochemical systems. Laboratory studies with RNA replicators have had some success with exploring the capacities of simple self-replicators, but these experiments are still limited in both capabilities and scope. Here, we use the digital evolution system Avida to explore the interplay between emergent replicators (rare randomly assembled self-replicators) and evolvability. We find that we can classify fixed-length emergent replicators in Avida into two classes based on functional analysis. One class is more evolvable in the sense of optimizing the replicators' replication abilities. However, the other class is more evolvable in the sense of acquiring evolutionary innovations. We tie this tradeoff in evolvability to the structure of the respective classes' replication machinery, and speculate on the relevance of these results to biochemical replicators.