Graphene (Gr)-based hot-electron transistors (GHETs) offer high potential for high-frequency applications due to the extremely thin nature of graphene as a base material. For the first time we present GHETs with excellent DC device characteristics and gigahertz operation achieved by an optimization of the emitter-base (E/B) composition. The optimized E/B composition enables more efficient injection of hot electrons into the base, thereby improving charge transport and reducing scattering losses. As a result, a record-high measured common-emitter current gain beta of 42 was achieved using a SiO₂/Gr E/B structure. Moreover, when using a MoS₂/Gr E/B junction the maximum output current is increased to record values of approximately 2000 A/cm², representing a significant improvement in performance over previous devices. Furthermore, cutoff frequencies of close to 1 GHz are determined for nonoptimized SiO₂/Gr-based devices. The experimentally observed device characteristics are very promising for future high-speed nanoelectronics.