Time-resolved measurements provide information about dynamical processes and are essential for studying complex physical, chemical and biological systems out of equilibrium. Electron probes in diffraction mode are uniquely suited to investigate correlated structural changes at surfaces, interfaces, and in atomically-thin materials. Ultrafast electron diffraction thus has a special role to play as a tool for scientists and engineers in the investigation of two-dimensional materials for modern technologies. This thesis reports the design, commissioning and first science results of a new ultrafast electron diffraction apparatus. The apparatus incorporates an extremely vacuum sensitive semiconductor electron source with a band gap matched to the wavelength of the photoemission laser. The source produces beams with state-of-the-art brightness at sub-relativistic acceleration energies. A single-electron-sensitive, high-dynamic-range, fast-frame-rate detector allows lock-in style data acquisition. Operated in this way, the experimental uncertainty of the apparatus is measured to be at the fundamental limit imposed by counting statistics. Time-resolved experiments performed on a twisted heterobilayer point to the potential for high-impact science results from the apparatus. This thesis also describes the design of a future upgrade to the apparatus that would enable high-resolution electron energy loss spectroscopy, making the apparatus sensitive to ultrafast changes in the electronic as well as structural properties of experimental samples.