To investigate the ingredients, which allow star-forming galaxies to present Lyalpha line in emission, we studied the kinematics and gas phase metallicity (Z) of the interstellar medium. We used multi-object NIR spectroscopy with Magellan/MMIRS to study nebular emission from z=2-3 star-forming galaxies discovered in 3 MUSYC fields. We detected emission lines from four active galactic nuclei and 13 high-z star-forming galaxies, including Halpha lines down to a flux of 4.E-17 erg/sec/cm^2. This yielded 7 new redshifts. The most common emission line detected is [OIII]5007, which is sensitive to Z. We were able to measure Z for 2 galaxies and to set upper(lower) limits for another 2(2). The Z values are consistent with 0.3<Z/Zsun<1.2. Comparing the Lyalpha central wavelength with the systemic redshift, we find Delta_v(Lyalpha-[OIII])=70-270 km/sec. High-redshift star-forming galaxies, Lyalpha emitting (LAE) galaxies, and Halpha emitters appear to be located in the low mass, high star-formation rate (SFR) region of the SFR versus stellar mass diagram, confirming that they are experiencing burst episodes of star formation, which are building up their stellar mass. Their Zs are consistent with the relation found for z<2.2 galaxies in the Z versus stellar mass plane. The measured Delta_v(Lyalpha-[OIII]) values imply that outflows of material, driven by star formation, could be present in the z=2-3 LAEs of our sample. Comparing with the literature, we note that galaxies with lower Z than ours are also characterized by similar Delta_v(Lyalpha-[OIII]) velocity offsets. Strong [OIII] is detected in many Lyalpha emitters. Therefore, we propose the Lyalpha/[OIII] flux ratio as a tool for the study of high-z galaxies; while influenced by Z, ionization, and Lyalpha radiative transfer in the ISM, it may be possible to calibrate this ratio to primarily trace one of these effects.