This paper experimentally demonstrates a design optimization of an evanescently-coupled waveguide germanium-on-silicon photodetector (PD) towards high-speed (> 30 Gb/s) applications. The resulting PD provides a responsivity of 1.09 A/W at 1550 nm, a dark current of 3.5 µA and bandwidth of 42.5 GHz at 2 V reverse-bias voltage. To optimize the PD, the impact of various design parameters on performance is investigated. A novel optimization methodology for the PD's responsivity based on the required bandwidth is developed. The responsivity of the PD is enhanced by enlarging its geometry and using off-centered contacts on top of the germanium, while an integrated peaking inductor mitigates the inherent bandwidth reduction from the responsivity optimization. The performance of the optimized PD and the conventional, smaller size non-optimized PD is compared to validate the optimization methodology. The sensitivity of the optimized PD improves by 3.2 dB over a smaller size non-optimized PD. The paper further discusses the impact of top metal contacts on the photodetector's performance.