Wireless networks are increasingly being used for latency-sensitive applications that require data delivery to be timely, efficient and reliable. This trend is primarily driven by the proliferation of wireless networks of real-time data-gathering sensor-actuator devices. This has led to a strong need to bring real-time concerns to the forefront of an integrated research thrust into wireless real-time systems. In this paper, we introduce and analyze a specific instance of the rich set of problems in this domain. We consider a wireless network serving real-time flows in which the underlying physical layer provides multiple transmission rates. Higher rates have more stringent SINR requirements and thus represent a trade-off between raw transmission speed and packet error rate. We adopt a first principles approach to the design of optimal real-time scheduling algorithms for such a multi-rate wireless network. We illustrate the inherent complexities of the problem through examples and obtain provably optimal structural results. We then characterize the optimal policy for an approximate model. Our theoretical analysis provides guidelines for heuristic scheduler design. Our initial work indicates that this is a rich problem domain with the potential for a unifying theory that integrates real-time requirements into multi-rate wireless network design.