The redundant manipulators' analytical solutions can be obtained by the parameterization method. Multiple parameterized joints and their corresponding parametric representations exist for a redundant manipulator. However, how to select the optimal parameterized joints has yet to be well-addressed. This paper delves into the mechanism of the parameterization method and proposes a method to select the optimal parametric representations to improve the motion planning performance of manipulators. We tested the proposed method on an 8-degree-of-freedom (DOF) manipulator. First, all feasible parametric representations are derived, followed by an approach to obtain solution manifolds. We then introduce a metric called the “feasible rate,” which characterizes the percentage of the solution manifold in the joint space. This metric is used to rapidly assess the influence of different parameterized joints on the manipulator's motion planning performance. To verify the proposed method's correctness, we evaluated the performance of different representations with the MOEA/D algorithm in solving the same path optimization problems based on the algorithm running time and overall motion magnitude of the manipulator. Our simulation results demonstrate that different selections of parameterized joints affect the motion planning performance, and the performance planned by the optimal parametric representation is up to four times greater than that of the worst one.