© 2019 IOP Publishing Ltd. Gravitational-wave astrophysics has the potential to be transformed by a global network of longer, colder, and thus more sensitive detectors. This network must be constructed to address a wide range of science goals, involving binary coalescence signals as well as signals from other, potentially unknown, sources. It is crucial to understand which network configurations - the number, type, and location of the detectors in the network - can best achieve these goals. In this work we examine a large number of possible three-detector networks, variously composed of Voyager, Einstein Telescope, and Cosmic Explorer detectors, and evaluate their performance against a number of figures of merit meant to capture a variety of future science goals. From this we infer that network performance, including sky localization, is determined most strongly by the type of detectors contained in the network, rather than the location and orientation of the facilities.