The Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) on the Large Binocular Telescope Interferometer will survey nearby stars for faint emission arising from ~300 K dust (exozodiacal dust), and aims to determine the exozodiacal dust luminosity function. HOSTS results will enable planning for future space telescopes aimed at direct spectroscopy of habitable zone terrestrial planets, as well as greater understanding of the evolution of exozodiacal disks and planetary systems. We lay out here the considerations that lead to the final HOSTS target list. Our target selection strategy maximizes the ability of the survey to constrain the exozodi luminosity function by selecting a combination of stars selected for suitability as targets of future missions and as sensitive exozodi probes. With a survey of approximately 50 stars, we show that HOSTS can enable an understanding of the statistical distribution of warm dust around various types of stars and is robust to the effects of varying levels of survey sensitivity induced by weather conditions.