When performing high-resolution imaging using a single-photon compressive technique, a long imaging time is required owing to numerous measurements and a large number of image-reconstruction calculations. We demonstrate a sampling-and-reconstruction-integrated residual codec network, namely SRIED-Net, for single-photon compressive imaging. We use the binarized fully connected layer as the first layer of the network and train it into a binary-measurement matrix to directly load onto the digital micromirror device for efficient compressive sampling. The remaining layers of the network are used to quickly reconstruct the compressed sensing image. We compare the effects of the compressive sampling rate, measurement matrix, and reconstruction algorithm on imaging performance through a series of simulations and system experiments. The experimental results show that SRIED-Net is superior to the current advanced iterative algorithm TVAL3 at a low measurement rate and that its imaging quality is similar to that of TVAL3 at a high measurement rate. It is superior to current deep-learning-based methods at all measurement rates.