Screw-based propulsion systems offer promising capabilities for amphibious mobility, yet face significant challenges in optimizing locomotion across water, granular materials, and transitional environments. This study presents a systematic investigation into the locomotion performance of various screw configurations in media such as dry sand, wet sand, saturated sand, and water. Through a principles-first approach to analyze screw performance, it was found that certain parameters are dominant in their impact on performance. Depending on the media, derived parameters inspired from optimizing heat sink design help categorize performance within the dominant design parameters. Our results provide specific insights into screw shell design and adaptive locomotion strategies to enhance the performance of screw-based propulsion systems for versatile amphibious applications.