This paper uses a systems engineering approach to address radiation exposure risks for humans on the first missions to Mars. Alternatives are reviewed in the areas of Mars mission architectures, various shielding technologies, and medical treatment options to help mitigate the risks of radiation doses received. The over-arching goal of this study is to determine if any alternatives will reduce astronaut radiation exposure on a mission to Mars to below the NASA space worker limits, while concurrently minimizing launch weight, costs, and risks. All alternatives are compared via a combination of existing trade studies and swing matrices. Using these tools, it is determined that boronated nitride nanotubes are the highest potential composite for vehicle shielding, and it is recommended that Martian regolith should be used in parallel for any long-stay by the crew on the Martian surface. Two medical countermeasures (Amifostine and Neupogen) are found to have the highest potential due for use, given that they are already FDA approved. It is also determined that no single shielding alternative will reduce crew exposure below existing limits, but further research may determine that a combination of composite shielding and regolith barriers may improve this outlook.