Large surveys with new-generation high-contrast imaging instruments are needed to derive the frequency and properties of exoplanet populations with separations from $sim$5 to 300 AU. A careful assessment of the stellar properties is crucial for a proper understanding of when, where, and how frequently planets form, and how they evolve. The sensitivity of detection limits to stellar age makes this a key parameter for direct imaging surveys. We describe the SpHere INfrared survey for Exoplanets (SHINE), the largest direct imaging planet-search campaign initiated at the VLT in 2015 in the context of the SPHERE Guaranteed Time Observations of the SPHERE consortium. In this first paper we present the selection and the properties of the complete sample of stars surveyed with SHINE, focusing on the targets observed during the first phase of the survey (from February 2015 to February 2017). This early sample composed of 150 stars is used to perform a preliminary statistical analysis of the SHINE data, deferred to two companion papers presenting the survey performance, main discoveries, and the preliminary statistical constraints set by SHINE. Based on a large database collecting the stellar properties of all young nearby stars in the solar vicinity (including kinematics, membership to moving groups, isochrones, lithium abundance, rotation, and activity), we selected the original sample of 800 stars that were ranked in order of priority according to their sensitivity for planet detection in direct imaging with SPHERE. The properties of the stars that are part of the early statistical sample were revisited, including for instance measurements from the GAIA Data Release 2.
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