We present metallicities, radial velocities, and near-infrared (NIR) spectral types for 447 M dwarfs determined from moderate resolution (R{approx}2000) NIR spectra obtained with the NASA Infrared Telescope Facility (IRTF)/SpeX. These M dwarfs are primarily 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 for each star and new spectral templates for the IRTF in the Y, 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 2.2{mu}m 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 -1.0dex<[Fe/H]<+0.35dex. We present a new color-color 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 2.2{mu}m. We used radial velocities of M dwarf binaries, observations at different epochs, and comparison between our measurements and precisely measured radial velocities to demonstrate a 4km/s accuracy.