  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 (being the majority BSGs) from the IACOB spectroscopic database. We
derive the projected rotational velocity ($v\sin i$) and macroturbulent
broadening ($v_{\rm mac}$) using IACOB-BROAD. We used FASTWIND computations to
derive effective temperatures ($T_{\rm eff}$), surface gravities,
microturbulences ($\xi$), Si and He 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, with 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$_\odot$ range. By investigating the
main characteristics of the $v\sin i$ distribution as a function of $T_{\rm
eff}$, 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 $\xi$, $v_{\rm mac}$ and the
spectroscopic luminosity. We also find that no more than 20% of the stars in
our sample have atmospheres clearly enriched in He, 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.
