This work reports an investigation of electron transport in monoclinic β-Ga2O3 based on a combination of density functional perturbation theory based-lattice dynamical computations, coupling calculation of lattice modes with collective plasmon oscillations, and Boltzmann theory-based transport calculations. The strong entanglement of the plasmon with the different longitudinal optical (LO) modes makes the role LO-plasmon coupling crucial for transport. The electron density dependence of the electron mobility in β-Ga2O3 is studied in the bulk material form and also in the form of a two-dimensional electron gas. Under high electron density, a bulk mobility of 182 cm2/V s is predicted, while in the 2DEG form, the corresponding mobility is about 418 cm2/V s when remote impurities are present at the interface and improves further as the remote impurity center moves away from the interface. The trend of the electron mobility shows promise for realizing high-electron mobility in dopant-isolated electron channels. The experimentally observed small anisotropy in mobility is traced through a transient Monte Carlo simulation. It is found that the anisotropy of the IR-active phonon modes is responsible for giving rise to the anisotropy in low-field electron mobility.