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Athletic robots demand a whole-body actuation system design that utilizes motors up to the boundaries of their performance. However, creating such robots poses challenges of integrating design principles and reasoning of practical design choices. This paper presents a design framework that guides designers to find optimal design choices to create an actuation system that can rapidly generate torques and velocities required to achieve a given set of tasks, by minimizing inertia and leveraging cooperation between actuators. The framework serves as an interactive tool for designers who are in charge of providing design rules and candidate components such as motors, reduction mechanism, and coupling mechanisms between actuators and joints. A binary integer linear optimization explores design combinations to find optimal components that can achieve a set of tasks. The framework is demonstrated with 200 optimal design studies of a biped with 5-degree-of-freedom (DoF) legs, focusing on the effect of achieving multiple tasks (walking, lifting), constraining the mass budget of all motors in the system and the use of coupling mechanisms. The result provides a comprehensive view of how design choices and rules affect reflected inertia, copper loss of motors, and force capability of optimal actuation systems.