A deep neural network (DNN) that can reliably model muscle responses from corresponding brain stimulation has the potential to increase knowledge of coordinated motor control for numerous basic science and applied use cases. Such cases include the understanding of abnormal movement patterns due to neurological injury from stroke, and stimulation based interventions for neurological recovery such as paired associative stimulation. In this work, potential DNN models are explored and the one with the minimum squared errors is recommended for the optimal performance of the M2M-Net, a network that maps transcranial magnetic stimulation of the motor cortex to corresponding muscle responses, using: a finite element simulation, an empirical neural response profile, a convolutional autoencoder, a separate deep network mapper, and recordings of multi-muscle activation. We discuss the rationale behind the different modeling approaches and architectures, and contrast their results. Additionally, to obtain a comparative insight of the trade-off between complexity and performance analysis, we explore different techniques, including the extension of two classical information criteria for M2M-Net. Finally, we find that the model analogous to mapping the motor cortex stimulation to a combination of direct and synergistic connection to the muscles performs the best, when the neural response profile is used at the input.