  The CARMENES radial velocity (RV) survey is observing 324 M dwarfs to search
for any orbiting planets. In this paper, we present the survey sample by
publishing one CARMENES spectrum for each M dwarf. These spectra cover the
wavelength range 520--1710nm at a resolution of at least $R > 80,000$, and we
measure its RV, H$\alpha$ emission, and projected rotation velocity. We present
an atlas of high-resolution M-dwarf spectra and compare the spectra to
atmospheric models. To quantify the RV precision that can be achieved in
low-mass stars over the CARMENES wavelength range, we analyze our empirical
information on the RV precision from more than 6500 observations. We compare
our high-resolution M-dwarf spectra to atmospheric models where we determine
the spectroscopic RV information content, $Q$, and signal-to-noise ratio. We
find that for all M-type dwarfs, the highest RV precision can be reached in the
wavelength range 700--900nm. Observations at longer wavelengths are equally
precise only at the very latest spectral types (M8 and M9). We demonstrate that
in this spectroscopic range, the large amount of absorption features
compensates for the intrinsic faintness of an M7 star. To reach an RV precision
of 1ms$^{-1}$ in very low mass M dwarfs at longer wavelengths likely requires
the use of a 10m class telescope. For spectral types M6 and earlier, the
combination of a red visual and a near-infrared spectrograph is ideal to search
for low-mass planets and to distinguish between planets and stellar
variability. At a 4m class telescope, an instrument like CARMENES has the
potential to push the RV precision well below the typical jitter level of
3-4ms$^{-1}$.
