In a volume-limited sample of 63 ultracool dwarfs of spectral type M7-M9.5, we have obtained high-resolution spectroscopy with UVES at the Very Large Telescope and HIRES at Keck Observatory. In this first paper we introduce our volume-complete sample from DENIS and 2MASS targets, and we derive radial velocities and space motion. Kinematics of our sample are consistent with the stars being predominantly members of the young disk. The kinematic age of the sample is 3.1Gyr. We find that six of our targets show strong Li lines implying that they are brown dwarfs younger than several hundred million years. Five of the young brown dwarfs were unrecognized before. Comparing the fraction of Li detections to later spectral types, we see a hint of an unexpected local maximum of this fraction at spectral type M9. It is not yet clear whether this maximum is due to insufficient statistics, or to a combination of physical effects including spectral appearance of young brown dwarfs, Li line formation, and the star formation rate at low masses.