We have completed a high-resolution (R=60,000) optical spectroscopic survey of 185 nearby M dwarfs identified using ROSAT data to select active, young objects with fractional X-ray luminosities comparable to or greater than Pleiades members. Our targets are drawn from the NStars 20-pc census and the Moving-M sample with distances determined from parallaxes or spectrophotometric relations. Nearly half of the resulting M dwarfs are not present in the Gliese catalog and have no previously published spectral types. We identified 30 spectroscopic binaries (SBs) from the sample, which have strong X-ray emission due to tidal spin-up rather than youth. This is equivalent to a 16% spectroscopic binary fraction, with at most a handful of undiscovered SBs. We estimate upper limits on the age of the remaining M dwarfs using spectroscopic youth indicators such as surface gravity-sensitive indices (CaH and K I). We find that for a sample of field stars with no metallicity measurements, a single CaH gravity index may not be sufficient, as higher metallicities mimic lower gravity. This is demonstrated in a sub-sample of metal-rich RV standards, which appear to have low surface gravity as measured by the CaH index, yet show no other evidence of youth. We also use additional youth diagnostics such as lithium absorption and strong H-alpha emission to set more stringent age limits. Eleven M dwarfs with no H-alpha emission or absorption are likely old (>400 Myr) and were caught during an X-ray flare. We estimate that our final sample of the 144 youngest and nearest low-mass objects in the field is less than 300 Myr old, with 30% of them being younger than 150 Myr and 4 very young (<10 Myr), representing a generally untapped and well-characterized resource of M dwarfs for intensive planet and disk searches.