  BA-type supergiants show a high potential as versatile indicators for modern
astronomy. The focus here is on the determination of accurate and precise
atmospheric parameters for a sample of 35 Galactic BA-type supergiants. Some
first applications include a recalibration of functional relationships between
spectral-type, intrinsic colours, bolometric corrections and effective
temperature, and an exploration of the reddening-free Johnson Q and Str\"omgren
[c_1] and beta-indices as photometric indicators for effective temperatures and
gravities of BA-type supergiants. An extensive grid of theoretical spectra is
computed based on a hybrid non-LTE approach. The atmospheric parameters are
derived spectroscopically by line-profile fits to high-resolution and high-S/N
spectra obtained at various observatories. Ionization equilibria of multiple
metals and the Stark-broadened H and the neutral He lines constitute our
primary indicators for the parameter determination, supplemented by
(spectro-)photometry. Data on Teff, logg, helium abundances, microturbulence,
macroturbulence and rotational velocities are presented. The interstellar
reddening and the ratio of total-to-selective extinction towards the stars are
determined. Our empirical spectral-type-Teff scale is steeper than reference
relations, the stars are significantly bluer, and bolometric corrections differ
significantly from established literature values. Photometric
Teff-determinations based on the reddening-free Q-index are found to be of
limited use for studies of BA-type supergiants because of large errors of
typically +-5%+-3% (1sigma statistical, 1sigma systematic), compared to a
spectroscopically achieved precision of 1-2%. The reddening-free [c_1]-index
and beta on the other hand are found to provide useful starting values for
further analyses, with uncertainties of +-1%+-2.5% in Teff, and +-0.04+-0.13dex
in log g. [abriged]
