InGaAs/InP single-photon avalanche diodes (SPADs) working in the regime of GHz clock rates are crucial components for the high-speed quantum key distribution (QKD). We have developed for the first time a compact, stable, and user-friendly tabletop InGaAs/InP single-photon detector system operating at a 1.25 GHz gate rate that fully integrates functions for controlling and optimizing SPAD performance. We characterize the key parameters of the detector system and test the long-term stability of the system for continuous operation of 75 h. The detector system can substantially enhance QKD performance and our present work paves the way for practical high-speed QKD applications.