The distinct influences of function, folding, and structure on the evolution of minimalist model proteins are studied by characterization of their evolutionary landscapes. Chains of up to 23 monomers on a two-dimensional square lattice are investigated by exhaustive enumeration of conformation and sequence space. In addition to common aspects of minimalist models, such as unique, stable native states and cooperative folding, functional model proteins have the novel feature of an explicit binding pocket. Fitness is defined through simple, physical characterization of the binding pocket. We characterize various properties of functional model proteins, focusing on their evolutionary landscapes, as defined by single point mutations, insertions, and deletions. The longer chains more closely resemble real proteins, having richer functional diversity and forming larger families of sequences. Although regions of evolutionary landscapes are often highly interconnected, we also observe so-called critical pathways, where evolution can only proceed through a single set of mutants.