In recent years, we have seen an uptrend in the popularity of UAVs driven by the desire to apply these aircraft to areas such as precision farming, surveying and mapping, search and rescue missions, and more. A major technical hurdle to overcome is that of drastically reducing the overall power consumption of these UAVs so they can be powered by solar arrays, and for long periods of time. The propulsion system plays a critical part in the overall power consumption of the UAV and therefore, it is necessary to determine the most optimal combination of possible propulsion system components for a given mission profile, i.e. propellers and motors. Hundreds of options are available for each of the components with generally non-scientific advice for choosing the proper combinations. A computationally-intensive, long-endurance solar-powered unmanned aircraft, the UIUC-TUM Solar Flyer is currently in development to enable a variety of all-daylight hour missions to be performed, involving continuous acquisition and processing of high resolution imagery. Currently, the critical choice has becomes what propulsion system components to use. A previously-developed mission-based propulsion system optimization tool and fixed-wind, electric unmanned aircraft propulsion system power model was used in this paper to select optimal combinations of possible components, i.e. propellers and motors, for the UIUC-TUM Solar Flyer, given a typical mission profile. Specifically, the optimization tool was able to match a motor-propeller combination that was 19% more efficient relative to the baseline (previously in use) combination for the given mission profile thrust and velocity design point. This paper first provides an overview of propulsion system optimization tool and system power model, including details regarding their validation. Then, recent wind tunnel performance testing of folding propellers is presented along with key observations. Next, a mission profile for the UIUC-TUM Solar Flyer was simulated and the resulting thrust and velocity design point are input into the propulsion system optimization tool to determine an optimally matched motor-propeller combination. Finally, a summary is given and future work is discussed.