Matching is an increasingly popular method of causal inference in observational data, but following methodological best practices has proven difficult for applied researchers. We address this problem by providing a simple graphical approach for choosing among the numerous possible matching solutions generated by three methods: the venerable ``Mahalanobis Distance Matching'' (MDM), the commonly used ``Propensity Score Matching'' (PSM), and a newer approach called ``Coarsened Exact Matching'' (CEM). In the process of using our approach, we also discover that PSM often approximates random matching, both in many real applications and in data simulated by the processes that fit PSM theory. Moreover, contrary to conventional wisdom, random matching is not benign: it (and thus PSM) can often degrade inferences relative to not matching at all. We find that MDM and CEM do not have this problem, and in practice CEM usually outperforms the other two approaches. However, with our comparative graphical approach and easy-to-follow procedures, focus can be on choosing a matching solution for a particular application, which is what may improve inferences, rather than the particular method used to generate it.