The mobile manipulator holds potential for executing multi-scene operational tasks through the collaborative movement of both the mobile base and manipulator. However, the conventional sequential base-manipulator control method for mobile manipulator is restricted in speed and gracefulness by the need for the mobile base to stop moving before the manipulator starts moving. In contrast, humans effortlessly handle such tasks while walking or running, simultaneously managing secondary tasks such as avoiding obstacles, optimizing posture, and monitoring the environment. Regrettably, mobile manipulators lack this agile finesse displayed by humans. To address this shortfall, this paper introduces a coordinated motion planning method that considers the manipulator and mobile base as a whole structure based on the task-priority redundancy resolution and considers the optimal mobile base placement in navigation. The simulation results demonstrate that the suggested method significantly improves the speed, reliably, and task completion efficiency of the mobile manipulator.