Blue supergiants (BSGs) are key objects for understanding the evolution of massive stars. However, discrepancies between theoretical predictions and empirical observations have opened up important questions yet to be answered. Studying statistically significant and unbiased samples of BSGs can help to improve the situation. We aim to 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. We derive the projected rotational velocity (vsin(i)) and the macroturbulent broadening (vmac) using IACOB-BROAD. We used FASTWIND computations to derive effective temperatures (Teff), surface gravities, microturbulences (xi), silicon and helium surface abundances, and the wind-strength parameter. We provide estimates of these quantities for the largest sample of Galactic luminous O9-B5 stars spectroscopically analyzed to date, comprising 527 targets. We find a drop in the relative number of stars at ~21 kK, coinciding with a scarcity of fast rotating stars below that temperature. We speculate that this feature might be roughly delineating the location of the Terminal-Age-Main-Sequence in the 15-85M_sol range. By investigating the main characteristics of the vsin(i) distribution 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. We find correlations between xi, v_mac and the spectroscopic luminosity. 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 sub-sample 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 towards lower temperatures.