  Young, low-mass stars in the solar neighborhood are vital for completing the
mass function for nearby, young coeval groups, establishing a more complete
census for evolutionary studies, and providing targets for direct-imaging
exoplanet and/or disk studies. We present properties derived from
high-resolution optical spectra for 336 candidate young nearby, low-mass stars.
These include measurements of radial velocities and age diagnostics such as
H$\alpha$ and Li $\lambda$6707 equivalent widths. Combining our radial
velocities with astrometry from Gaia DR2, we provide full 3D kinematics for the
entire sample. We combine the measured spectroscopic youth information with
additional age diagnostics (e.g., X-ray and UV fluxes, CMD positions) and
kinematics to evaluate potential membership in nearby, young moving groups and
associations. We identify 78 objects in our sample as bonafide members of 10
different moving groups, 15 of which are completely new members or have had
their group membership reassigned. We also reject 44 previously proposed
candidate moving group members. Furthermore, we have newly identified or
confirmed the youth of numerous additional stars that do not belong to any
currently known group, and find 69 co-moving systems using Gaia DR2 astrometry.
We also find evidence that the Carina association is younger than previously
thought, with an age similar to the $\beta$ Pictoris moving group ($\sim$22
Myr).
