  This is the first of a series of papers devoted to the investigation of a
large sample of brightest cluster galaxies (BCGs), their kinematic and stellar
population properties, and the relationships between those and the properties
of the cluster. We have obtained high signal-to-noise ratio, long-slit spectra
of these galaxies with Gemini and WHT with the primary purpose of investigating
their stellar population properties. This paper describes the selection methods
and criteria used to compile a new sample of galaxies, concentrating on BCGs
previously classified as containing a halo (cD galaxies), together with the
observations and data reduction. Here, we present the full sample of galaxies,
and the measurement and interpretation of the radial velocity and velocity
dispersion profiles of 41 BCGs. We find clear rotation curves for a number of
these giant galaxies. In particular, we find rapid rotation (> 100 km/s) for
two BCGs, NGC6034 and NGC7768, indicating that it is unlikely that they formed
through dissipationless mergers. Velocity substructure in the form of
kinematically decoupled cores is detected in 12 galaxies, and we find five
galaxies with velocity dispersion increasing with radius. The amount of
rotation, the velocity substructure and the position of BCGs on the
anisotropy-luminosity diagram are very similar to those of "ordinary" giant
ellipticals in high density environments.
