The design of nature reserves is becoming, more and more, a crucial task for ensuring the conservation of endangered wildlife. In order to guarantee the preservation of species and a general ecological functioning, the designed reserves must typically verify a series of spatial requirements. Among the required characteristics, practitioners and researchers have pointed out two crucial aspects: (i) connectivity, so as to avoid spatial fragmentation, and (ii) the design of buffer zones surrounding (or protecting) so-called core areas. In this paper, we introduce the Generalized Reserve Set Covering Problem with Connectivity and Buffer Requirements. This problem extends the classical Reserve Set Covering Problem and allows to address these two requirements simultaneously. A solution framework based on Integer Linear Programming and branch-and-cut is developed. The framework is enhanced by valid inequalities, a construction and a primal heuristic and local branching. The problem and the framework are presented in a modular way to allow practitioners to select the constraints fitting to their needs and to analyze the effect of e.g., only enforcing connectivity or buffer zones. An extensive computational study on grid-graph instances and real-life instances based on data from three states of the U.S. and one region of Australia is carried out to assess the suitability of the proposed model to deal with the challenges faced by decision-makers in natural reserve design. In the study, we also analyze the effects on the structure of solutions when only enforcing connectivity or buffer zones or just solving a generalized version of the classical Reserve Set Covering Problem. The results show, on the one hand, the flexibility of the proposed models to provide solutions according to the decision-makers’ requirements, and on the other hand, the effectiveness of the devised algorithm for providing good solutions in reasonable computing times.