  Blue supergiants (BSGs) are important objects to study the intermediate
phases of massive star evolution, helping to constrain evolutionary models.
However, the lack of a holistic study of a statistically significant and
unbiased sample of these objects makes several long-standing questions about
their nature to remain unsolved. The present and other upcoming papers of the
IACOB series are focused in studying - from a pure empirical point of view - a
sample of 500 Galactic O9 - B9 stars with luminosity classes I and II (plus 250
late O- and early B-type stars with luminosity classes III, IV and V) and
covering distances up to 4 kpc from the Sun. We compile an initial set of 11000
high-resolution spectra of 1600 Galactic late O- and B-type stars. We use a new
novel spectroscopic strategy based on a simple fitting of the Hbeta line to
select stars in a specific region of the spectroscopic HR diagram. We evaluate
the completeness of our sample using the Alma Luminous Star catalog (ALS III)
and Gaia-DR3 data. We show the benefits of the proposed strategy for
identifying BSGs descending from stellar objects born as O-type stars, in the
context of single star evolution. The resulting sample reaches a high level of
completeness with respect to the ALS III catalog, gathering the 80% for all-sky
targets brighter than Bmag < 9 located within 2 kpc. However, we identify the
need for new observations in specific regions of the Southern hemisphere. In
conclusion, we have explored a very fast and robust method to select BSGs,
providing a valuable tool for large spectroscopic surveys like WEAVE-SCIP or
4MIDABLE-LR, and highlighting the risk of using spectral classifications from
the literature. Upcoming works will make use of this large and homogeneous
spectroscopic sample to study specific properties of these stars in detail. We
initially provide first results about their rotational properties.
