Context. The IACOB and OWN surveys are two ambitious, complementary observational projects which have made available a large multi-epoch spectroscopic database of optical high resolution spectra of Galactic massive O-type stars. Aims: Our aim is to study the full sample of (more than 350) O stars surveyed by the IACOB and OWN projects. As a first step towards this aim, we have performed the quantitative spectroscopic analysis of a subsample of 128 stars included in the modern grid of O-type standards for spectral classification. The sample comprises stars with spectral types in the range O3-O9.7 and covers all luminosity classes. Methods: We used the semi-automatized IACOB-BROAD and IACOB-GBAT/FASTWIND tools to determine the complete set of spectroscopic parameters that can be obtained from the optical spectrum of O-type stars. A quality flag was assigned to the outcome of the IACOB-GBAT/FASTWIND analysis for each star, based on a visual evaluation of how the synthetic spectrum of the best fitting FASTWIND model reproduces the observed spectrum. We also benefitted from the multi-epoch character of the IACOB and OWN surveys to perform a spectroscopic variability study of the complete sample, providing two different flags for each star accounting for spectroscopic binarity as well as variability of the main wind diagnostic lines. Results: We obtain - for the first time in a homogeneous and complete manner - the full set of spectroscopic parameters of the "anchors" of the spectral classification system in the O star domain. We provide a general overview of the stellar and wind parameters of this reference sample, as well as updated recipes for the SpT-Teff and SpT-log g calibrations for Galactic O-type stars. We also propose a distance-independent test for the wind-momentum luminosity relationship. We evaluate the reliability of our semi-automatized analysis strategy using a subsample of 40 stars extensively studied in the literature, and find a fairly good agreement between our derived effective temperatures and gravities and those obtained by means of more traditional "by-eye" techniques and different stellar atmosphere codes. The overall agreement between the synthetic spectra associated with the IACOB-GBAT/FASTWIND best fitting models and the observed spectra is good for most of the analyzed targets, but 46 stars out of the 128 present a particular behavior of the wind diagnostic lines that cannot be reproduced by our grid of spherically symmetric unclumped models. These are potential targets of interest for more detailed investigations of clumpy winds and/or the existence of additional circumstellar emitting components contaminating the wind diagnostic lines (e.g., disks, magnetospheres). Last, our spectroscopic variability study has led to the detection of clear or likely signatures of spectroscopic binarity in 27% of the stars and small amplitude radial velocity variations in the photospheric lines of another 30%. Additionally, 31% of the investigated stars show variability in the wind diagnostic lines. Tables D.1 and D.2 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/613/A65