  We present metallicities, radial velocities and near-infrared spectral types
for 447 M dwarfs determined from moderate resolution (R~2000) near-infrared
(NIR) spectra obtained with IRTF/SpeX. These M dwarfs are targets of the MEarth
Survey, a transiting planet survey searching for super Earths around
mid-to-late M dwarfs within 33pc. We present NIR spectral types and new IRTF
spectral templates in the Z, J, H and K-bands, created using M dwarfs with
near-solar metallicities. We developed two spectroscopic distance calibrations
that use NIR spectral type or an index based on the curvature of the K-band
continuum. Our distance calibration has a scatter of 14%. We searched 27 NIR
spectral lines and 10 spectral indices for metallicity sensitive features,
taking into account correlated noise in our estimates of the errors on these
parameters. We calibrated our relation using 36 M dwarfs in common proper pairs
with an F, G or K-type star of known metallicity. We validated the physical
association of these pairs using proper motions, radial velocities and
spectroscopic distance estimates. Our resulting metallicity calibration uses
the sodium doublet at 2.2um as the sole indicator for metallicity. It has an
accuracy of 0.12dex inferred from the scatter between the metallicities of the
primaries and the estimated metallicities of the secondaries. Our relation is
valid for NIR spectral types from M1V to M5V and for -1.0<[Fe/H]<+0.35dex. We
present a new metallicity relation using J-H and J-K colors that directly
relates two observables: the distance from the M dwarf main sequence and
equivalent width of the sodium line at 2.2um. We measured radial velocities by
modeling telluric features to determine the absolute wavelength calibration of
our spectra, and used M dwarf binaries, observations at different epochs, and
comparison to precisely measured radial velocities to demonstrate 4.4km/s
accuracy.
