Deep neural network (DNN)-based approaches to acoustic echo cancellation (AEC) and hybrid speech enhancement systems have gained increasing attention recently, introducing significant performance improvements to this research field. Using the fully convolutional recurrent network (FCRN) architecture that is among state of the art topologies for noise reduction, we present a novel deep residual echo suppression and noise reduction with up to four input signals as part of a hybrid speech enhancement system with a linear frequency domain adaptive Kalman filter AEC. In an extensive ablation study, we reveal trade-offs with regard to echo suppression, noise reduction, and near-end speech quality, and provide surprising insights to the choice of the FCRN inputs: In contrast to often seen input combinations for this task, we propose not to use the loudspeaker reference signal, but the enhanced signal after AEC, the microphone signal, and the echo estimate, yielding improvements over previous approaches by more than 0.2 PESQ points.