Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by networks belonging to the same broad class, such as the class of social networks or the class of biological networks. At a finer scale of classification within each such class, networks describing more similar systems tend to have more similar features. This occurs presumably because networks representing similar purposes or constructions would be expected to be generated by a shared set of domain specific mechanisms, and it should therefore be possible to classify these networks into categories based on their features at various structural levels. Here we describe and demonstrate a new, hybrid approach that combines manual selection of features of potential interest with existing automated classification methods. In particular, selecting well-known and well-studied features that have been used throughout social network analysis and network science and then classifying with methods such as random forests that are of special utility in the presence of feature collinearity, we find that we achieve higher accuracy, in shorter computation time, with greater interpretability of the network classification results.