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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 β≃-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 NaI/CaII 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 Lymanα 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.