An exhaustive optimization method is developed to minimize the power consumption for a propeller-driven electrical aircraft. The method finds the optimal value for a wide range of geometrical and operational parameters for a target thrust and airspeed. The optimization routine employs BEM for propeller predictions fed with aerodynamic airfoil data obtained from a proposed combined CFD-Montgomerie method which is also validated, furthermore several corrections to account for compressibility, three dimensional, viscous and Reynolds number effects are implemented. This BEM model showed an adequate fitting with experimental data. Additionally, Goldstein optimization via Vortex Theory is employed to design pitch and chord distributions minimizing the induced losses of the propeller. The optimization algorithm is validated through a study case where an existent optimization problem is approached leading to very similar results. Some trends and insights are obtained and discussed from the study case regarding the design of an optimal propulsion system. Finally, CFD simulations of the study case are carried out showing a slight relative error of BEM.