Identifying the optimal design of a new launch vehicle is most important since design decisions made in the early development phase limit the vehicles' later performance and determines the associated costs. Reusing the first stage via retro-propulsive landing increases the complexity even more. Therefore, we develop an optimization framework for partially reusable launch vehicles, which enables multidisciplinary design studies. The framework contains suitable mass estimates of all essential subsystems and a routine to calculate the needed propellant for the ascent and landing maneuvers. For design optimization, the framework can be coupled with a genetic algorithm. The overall goal is to reveal the implications of different propellant combinations and objective functions on the launcher's optimal design for various mission scenarios. The results show that the optimization objective influences the most suitable propellant choice and the overall launcher design, concerning staging, weight, size, and rocket engine parameters. In terms of gross lift-off weight, liquid hydrogen seems to be favorable. When optimizing for a minimum structural mass or an expandable structural mass, hydrocarbon-based solutions show better results. Finally, launch vehicles using a hydrocarbon fuel in the first stage and liquid hydrogen in the upper stage are an appealing alternative, combining both fuels' benefits.