We conduct a rigorous examination of the nearby red supergiant Betelgeuse by drawing on the synthesis of new observational data and three different modeling techniques. Our observational results include the release of new, processed photometric measurements collected with the space-based Solar Mass Ejection Imager instrument prior to Betelgeuse's recent, unprecedented dimming event. We detect the first radial overtone in the photometric data and report a period of 185+/-13.5d. Our theoretical predictions include self-consistent results from multi-timescale evolutionary, oscillatory, and hydrodynamic simulations conducted with the Modules for Experiments in Stellar Astrophysics software suite. Significant outcomes of our modeling efforts include a precise prediction for the star's radius: 764_-62_^+116^R_{sun}_. In concert with additional constraints, this allows us to derive a new, independent distance estimate of 168_-15_^+27^pc and a parallax of {pi}=5.95_-0.85_^+0.58^mas, in good agreement with Hipparcos but less so with recent radio measurements. Seismic results from both perturbed hydrostatic and evolving hydrodynamic simulations constrain the period and driving mechanisms of Betelgeuse's dominant periodicities in new ways. Our analyses converge to the conclusion that Betelgeuse's ~400d period is the result of pulsation in the fundamental mode, driven by the {kappa}-mechanism. Grid-based hydrodynamic modeling reveals that the behavior of the oscillating envelope is mass-dependent, and likewise suggests that the nonlinear pulsation excitation time could serve as a mass constraint. Our results place {alpha} Orionis definitively in the early core helium-burning phase of the red supergiant branch. We report a present-day mass of 16.5-19M_{sun}_ --slightly lower than typical literature values.