  We aim at analysing systematically the distribution and physical properties
of neutral and mildly ionised gas in the Milky Way halo, based on a large
absorption-selected data set. Multi-wavelength studies were performed combining
optical absorption line data of CaII and NaI with follow-up HI 21-cm emission
line observations along 408 sight lines towards low- and high-redshift QSOs. We
made use of archival optical spectra obtained with UVES/VLT. HI data were
extracted from the Effelsberg-Bonn HI survey and the Galactic All-Sky survey.
For selected sight lines we obtained deeper follow-up observations using the
Effelsberg 100-m telescope. CaII (NaI) halo absorbers at intermediate and high
radial velocities are present in 40-55% (20-35%) of the sightlines, depending
on the column density threshold chosen. Many halo absorbers show
multi-component absorption lines, indicating the presence of sub-structure. In
65% of the cases, absorption is associated with HI 21-cm emission. The CaII
(NaI) column density distribution function follows a power-law with a slope of
-2.2 (-1.4). Our absorption-selected survey confirms our previous results that
the Milky Way halo is filled with a large number of neutral gas structures
whose high column density tail represents the population of common HI high- and
intermediate-velocity clouds seen in 21-cm observations. We find that CaII/NaI
column density ratios in the halo absorbers are typically smaller than those in
the Milky Way disc, in the gas in the Magellanic Clouds, and in damped
Lyman-alpha systems. The small ratios (prominent in particular in high-velocity
components) indicate a lower level of Ca depletion onto dust grains in Milky
Way halo absorbers compared to gas in discs and inner regions of galaxies.
