Aims: We present basic atmospheric parameters (Teff, log g, vt, and [Fe/H]) as well as luminosities, masses, radii, and absolute radial velocities for 348 stars, presumably giants, from the ~1000 star sample observed within the Penn State-Toruń Centre for Astronomy Planet Search with the High Resolution Spectrograph of the 9.2 m Hobby-Eberly Telescope. The stellar parameters (luminosities, masses, radii) are key to properly interpreting newly discovered low-mass companions, while a systematic study of the complete sample will create a basis for future statistical considerations concerning the appearance of low-mass companions around evolved low- and intermediate-mass stars. Methods: The atmospheric parameters were derived using a strictly spectroscopic method based on the LTE analysis of equivalent widths of Fe I and Fe II lines. With existing photometric data and the Hipparcos parallaxes, we estimated stellar masses and ages via evolutionary tracks fitting. The stellar radii were calculated from either estimated masses and the spectroscopic log g or from the spectroscopic Teff and estimated luminosities. The absolute radial velocities were obtained by cross-correlating spectra with a numerical template. Results: We completed the spectroscopic analysis for 332 stars, 327 of which were found to be giants. A simplified analysis was applied to the remaining 16 stars, which had incomplete data. The results show that our sample is composed of stars with effective temperatures ranging from 4055 K to 6239 K, with log g between 1.39 and 4.78 (5 dwarfs were identified). The estimated luminosities are between log L/L⊙ = -1.0 and 3 and lead to masses ranging from 0.6 to 3.4 M⊙. Only 63 stars with masses larger than 2 M⊙ were found. The radii of our stars range from 0.6 to 52 R⊙ with the vast majority between 9-11 R⊙. The stars in our sample are generally less metal-abundant than the Sun with median [Fe/H] = -0.15. The estimated uncertainties in the atmospheric parameters were found to be comparable to those reached in other studies. However, due to lack of precise parallaxes, the stellar luminosities and, in turn, the masses are far less precise, within 0.2 M⊙ in best cases and 0.3 M⊙ on average. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.Tables 1 and 5 are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/547/A91