Accurate simulation of wave propagation is crucial for various engineering and scientific applications. However, achieving this accuracy is challenging due to numerical dispersion errors that arise from both spatial and temporal discretizations. This study presents a comprehensive dispersion analysis of the velocity-based Space-Time Finite Element Method (v-ST/FEM), aiming to provide practical guidelines for its application to wave propagation problems. In this analysis, the contributions of spatial and temporal discretizations to the total dispersion error are systematically separated and quantified. The Relative Phase Speed Error (RPSE) is introduced as a unified metric for assessing these errors. By visualizing the RPSE contour across different numerical settings, we clarify the relationship between mesh size, time-step size, and interpolation order in relation to dispersion error. Interestingly, unlike conventional time integration schemes, where temporal errors often dominate, the v-ST/FEM is mainly affected by spatial discretization. Therefore, increasing the spatial interpolation order significantly reduces dispersion errors and enables nearly oscillation-free solutions over a wide range of discretization parameters. The theoretical insights gleaned from the RPSE contour are validated through several numerical examples, which include both smooth and discontinuous excitations. The RPSE contours not only predict the magnitude of the dispersion error but also correlate with observable oscillation patterns in the numerical solutions—positive RPSE results in head oscillations, while negative RPSE leads to tail oscillations. This understanding allows practitioners to diagnose and mitigate numerical artifacts by referencing the RPSE contour and adjusting the discretization parameters accordingly. Based on this analysis, we propose a set of practical guidelines for the v-ST/FEM, highlighting the advantages of high-order elements. This framework effectively connects theoretical dispersion analysis with practical implementation, providing a valuable resource for researchers and engineers who utilize space-time methods in wave propagation simulations.