Context. Blue supergiants (BSGs) are key objects for understanding the evolution of massive stars, which play a crucial role in the evolution of galaxies. However, discrepancies between theoretical predictions and empirical observations have opened up important questions yet to be answered. Studying statistically significant and unbiased samples of these objects can help to improve the situation. Aims. We perform a homogeneous and comprehensive quantitative spectroscopic analysis of a large sample of Galactic luminous blue stars (a majority of which are BSGs) from the IACOB spectroscopic database, providing crucial parameters to refine and improve theoretical evolutionary models. Methods. We derived the projected rotational velocity (υ sin i) and macroturbulent broadening (υmac) using IACOB-BROAD, which combines Fourier transform and line-profile fitting techniques. We compared high-quality optical spectra with state-of-the-art simulations of massive star atmospheres computed with the FASTWIND code. This comparison allowed us to derive effective temperatures (Teff), surface gravities (log 𝑔), microturbulences (ξ), surface abundances of silicon and helium, and to assess the relevance of stellar winds through a wind-strength parameter (log Q). Results. We provide estimates and associated uncertainties of the above-mentioned quantities for the largest sample of Galactic luminous O9 to B5 stars spectroscopically analyzed to date, comprising 527 targets. We find a clear drop in the relative number of stars at Teff ≈ 21 kK, coinciding with a scarcity of fast rotating stars below that temperature. We speculate that this feature (roughly corresponding to B2 spectral type) might be roughly delineating the location of the empirical terminal-age main sequence in the mass range between 15 and 85 M⊙. By investigating the main characteristics of the υ sin i distribution of O stars and BSGs as a function of Teff, we propose that an efficient mechanism transporting angular momentum from the stellar core to the surface might be operating along the main sequence in the high-mass domain. We find correlations between ξ,υmac and the spectroscopic luminosity 𝓛 (defined as Teff4 / g). We also find that no more than 20% of the stars in our sample have atmospheres clearly enriched in helium, and suggest that the origin of this specific subsample might be in binary evolution. We do not find clear empirical evidence of an increase in the wind strength over the wind bi-stability region toward lower Teff.