Automated machine learning (AutoML) streamlines the creation of ML models. While most methods select the "best" model based on predictive quality, it's crucial to acknowledge other aspects, such as interpretability and resource consumption. This holds particular importance in the context of deep neural networks (DNNs), as these models are often perceived as computationally intensive black boxes. In the challenging domain of time series forecasting, DNNs achieve stunning results, but specialized approaches for automatically selecting models are scarce. In this paper, we propose AutoXPCR - a novel method for automated and explainable multi-objective model selection. Our approach leverages meta-learning to estimate any model's performance along PCR criteria, which encompass (P)redictive error, (C)omplexity, and (R)esource demand. Explainability is addressed on multiple levels, as our interactive framework can prioritize less complex models and provide by-product explanations of recommendations. We demonstrate practical feasibility by deploying AutoXPCR on over 1000 configurations across 114 data sets from various domains. Our method clearly outperforms other model selection approaches - on average, it only requires 20% of computation costs for recommending models with 90% of the best-possible quality.