Laser-driven shock waves in matter propagate with multiple kilometers per second and therefore require sources like a laser-driven backlighter, which emit the X-rays within picoseconds, to be able to capture sharp images. The small spatial extent of shocks in low-density materials pose challenges on the imaging setup. In this work, we present a design process for a single-shot X-ray phase-contrast imaging system geared towards these objects, consisting of a two-grating Talbot interferometer and a digital X-ray detector. This imaging system is optimized with respect to the detectable refraction angle of the X-rays induced by an object, which implies a high phase sensitivity. Therefore, an optimization parameter is defined that considers experimental constraints such as the limited number of photons, the required magnification, the size and spectrum of the X-ray source, and the visibility of the moiré fringes. In this way, a large parameter space is sampled and a suitable imaging system is chosen. During a campaign at the PHELIX high-power laser facility a static test sample was imaged which is used to benchmark the optimization process and the imaging system under real conditions. The results show good agreement with the predicted performance, which demonstrates the reliability of the presented design process. Likewise, the process can be adapted to other types of laser experiments or X-ray sources and is not limited to the application presented here.