Significance Humoral immunity relies on the mutation and selection of B cells to better recognize pathogens. This affinity maturation process produces cells with diverse recognition capabilities. Examining optimal immune strategies that maximize the long-term immune coverage at a minimal metabolic cost, we show when the immune system should mount a de novo response rather than rely on existing memory cells. Our theory recapitulates known modes of the B cell response, predicts the empirical form of the distribution of clone sizes, and rationalizes as a trade-off between metabolic and immune costs the antigenic imprinting effects that limit the efficacy of vaccines (original antigenic sin). Our predictions provide a framework to interpret experimental results that could be used to inform vaccination strategies.