The recent discovery that van der Waals-bonded magnetic materials retain long range magnetic ordering down to a single layer stimulates a thorough Raman spectroscopic study of such materials, including FePS₃ and V-doped WS₂. Bulk FePS₃ was shown to be a quasi-2D Ising antiferromagnet, with additional features in the Raman spectra emerging below the Néel temperature (T_N ~ 120 K). Using temperature and magnetic field-dependent Raman spectroscopy as an optical probe of magnetic structure, we demonstrate that one of these Raman-active modes (ψ₄) below T_N is a magnon with a frequency of ~ 3.7 THz (~122 cm^-1). Contrary to previous work, which interpreted this feature as a phonon, our Raman data shows the expected frequency shifting and splitting of the magnon as a function of temperature and magnetic field, respectively, where we find the g-factor ~2. Other Raman-active modes emerging below T_N are attributed to zone-folded phonons in the antiferromagnetic state. The anomalous temperature dependence of these modes along with an analysis of temperature dependent magnetization data, suggests a persistence of short-range magnetic order above T_N. In contrast to antiferromagnetic FePS₃, the transition metal dichalcogenide WS₂ doped is found to be ferromagnetic when doped with vanadium down to the monolayer. We compare our magneto-Raman measurements on V-doped WS₂ to circularly-polarized magneto-PL measurements.