We investigate the structural, electronic, vibrational, power, and transport properties of the β allotrope of Ga2O3 from first principles. We find phonon frequencies and elastic constants that reproduce the correct band ordering, in agreement with experiment. We use the Boltzmann transport equation to compute the intrinsic electron and hole drift mobility and obtain room-temperature values of 258 and 1.2 cm2/Vs, respectively, as well as 6300 and 13 cm2/Vs at 100 K. Through a spectral decomposition of the scattering contribution to the inverse mobility, we find that multiple longitudinal-optical modes of Bu symmetry are responsible for the electron mobility of β-Ga2O3 but that many acoustic modes also contribute, making it essential to include all scattering processes in the calculations. Using the von Hippel low-energy criterion, we computed the breakdown field to be 5.8 MV/cm at room temperature, yielding a Baliga figure of merit of 1250 with respect to silicon, ideal for high-power electronics. This work presents a general framework to predictively investigate novel high-power electronic materials.