Aims: One of the main scientific drivers for ESPRESSO, Échelle SPectrograph, is the detection and characterization of Earth-class exoplanets. With this goal in mind, the ESPRESSO guaranteed time observations (GTO) Catalog identifies the best target stars for a blind search for the radial velocity (RV) signals caused by Earth-class exoplanets. Methods: Using the most complete stellar catalogs available, we screened for the most suitable G, K, and M dwarf stars for the detection of Earth-class exoplanets with ESPRESSO. For most of the stars, we then gathered high-resolution spectra from new observations or from archival data. We used these spectra to spectroscopically investigate the existence of any stellar binaries, both bound or background stars. We derived the activity level using chromospheric activity indexes using log (R'HK), as well as the projected rotational velocity v sin i. For the cases where planet companions are already known, we also looked at the possibility that additional planets may exist in the host's habitable zone using dynamical arguments. Results: We estimated the spectroscopic contamination level, v sin i, activity, stellar parameters and chemical abundances for 249 of the most promising targets. Using these data, we selected 45 stars that match our criteria for detectability of a planet like Earth. The stars presented and discussed in this paper constitute the ESPRESSO GTO catalog for the RV blind search for Earth-class planets. They can also be used for any other work requiring a detailed spectroscopic characterization of stars in the solar neighborhood. Based on observations collected at the La Silla Observatory, ESO(Chile), with the HARPS spectrograph at the 3.6-m telescope for program 97.C - 0561(A), data obtained at the Paranal Observatory of the European Southern Observatory with UVES at VLT for program 097.C - 0561(B) and data obtained at the TNG telescope for program A33TAC_7, and also 95 programs. The large list is presented in Table B.1.