Monoceros R2 (Mon R2) is one of the closest large active star-forming regions. This extremely young and partially embedded region provides an excellent laboratory for studying star formation and the early evolution of young stellar objects (YSOs). In this paper, we conduct an optical study of the greater Mon R2 region. Beginning with 1690 previously identified candidate YSOs, we used 496 sources with good proper motions and parallaxes from Gaia Data Release (DR) 3 to determine the astrometric properties for likely members of Mon R2. We then used both astrometric and photometric (isochronal and variability) criteria to determine that 308 of these stars are highly probable members. Using the same criteria, we considered a broad area search around Mon R2 in Gaia DR3 and separated candidate members from field stars. In total, we selected 651 likely new cluster members that had been missed in the previous X-ray and infrared excess selection techniques used in the past to establish cluster membership. Revised astrometric properties of the cluster were found using the combined sample of ~959 highly probable member stars. For the literature plus the new candidate member list, optical light curves were compiled from the Zwicky Transient Facility. For 470 identified variable sources, we attempted classification based on the flux asymmetry (M) and quasiperiodicity (Q) metrics. We find that Mon R2 is dominated by quasiperiodic symmetric variables, with aperiodic sources also a significant population. A few tens of large-amplitude variables are identified that may be of interest for further study.