We present echelle long-slit optical spectra of a sample of objects evolving off the asymptotic giant branch (AGB), most of them in the preplanetary nebula ( PPN ) phase, obtained with the ESI and MIKE spectrographs at the 10 m Keck II and 6.5 m Magellan-I telescopes, respectively. The total wavelength range covered with ESI (MIKE) is $3900Y10900 8 ($3600Y7200 8). In this paper, we focus our analysis mainly on the H profiles. Prominent H emission is detected in half of the objects, most of which show broad H wings (with total widths of up to $4000 km s À1 ). In the majority of the H -emission sources, fast, post-AGB winds are revealed by P-Cygni profiles. In $37% of the objects H is observed in absorption. In almost all cases, the absorption profile is partially filled with emission, leading to complex, structured profiles that are interpreted as an indication of incipient post-AGB mass loss. The rest of the objects ($13%) are H nondetections. We investigate correlations between the H profile and different stellar and envelope parameters. All sources in which H is seen mainly in absorption have F-G type central stars, whereas sources with intense H emission span a larger range of spectral types from O to G, with a relative maximum around B, and also including very late C types. Shocks may be an important excitation/ionization agent of the close stellar surroundings for objects with late type central stars. Sources with pure emission or P Cygni H profiles have larger J À K color excess than objects with H mainly in absorption, which suggests the presence of warm dust near the star in the former. The two classes of profile sources also segregate in the IRAS color-color diagram in a way that intense H -emitters have dust grains with a larger range of temperatures. Spectral classification of the central stars in our sample is presented. For a subsample (13 objects), the stellar luminosity has been derived from the analysis of the O i 7771Y7775 8 infrared triplet. The location in the HR diagram of most of these targets, which represent $30% of the whole sample, is consistent with relatively high final (and, presumably, initial) masses in the range M f $ 0:6 Y0:9 M (M i $ 3Y 8 M ).