The Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) on the Large Binocular Telescope Interferometer (LBTI) will survey nearby stars for faint exozodiacal dust (exozodi). This warm circumstellar dust, analogous to the interplanetary dust found in the vicinity of the Earth in our own system, is produced in comet breakups and asteroid collisions. Exozodi will be the major source of astrophysical noise for a future space telescope aimed at direct imaging and spectroscopy of habitable zone terrestrial planets (exo-Earths). About 20% of nearby field stars have cold dust coming from planetesimals at large distances from the stars (Eiroa et al. 2013). Much less is known about exozodi; current detection limits for individual stars are at best ~ 500 times our solar system's level (aka. 500 zodi). LBTI-HOSTS will be the first survey capable of measuring exozodi at the 10 zodi level (3s). Detections of warm dust will also reveal new information about planetary system architectures and evolution. We describe the target star selection by the LBTI Science Team to satisfy the goals of the HOSTS survey - to inform mission design and target selection for a future exo-Earth mission. We are interested in both 1) actual stars likely to be observed by such a mission and 2) stars whose observation will enable sensible extrapolations for stars that cannot be observed with LBTI. We integrated two approaches to generate the HOSTS target list. The mission-driven approach concentrates on F, G, and K-type stars that are the best targets for future direct observations of exo-Earths, thereby providing model-independent "ground truth" dust observations. However, not every potential target of a future exo-Earth mission can be observed with LBTI. The sensitivity-driven approach selects targets based on maximizing the exozodi sensitivity that can be achieved, without consideration of exo-Earth mission constraints. This naturally chooses more luminous stars (A and early F-type stars). In both cases, all stars are close enough to Earth such that their habitable zones are resolvable by LBTI and bright enough at N-band (10 µm) to provide excellent sensitivity. We also discuss observational and astrophysical motivations for excluding binaries of certain separations.