The Magellan-TESS Survey. I. Survey Description and Midsurvey Results* * This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. † †Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.