Edge intelligence is about enabling deep learning applications to run on edge platforms, often under strict Quality of Service (QoS) constraints (e.g., deadlines and accuracy). The heterogeneity and limited computational and energy capacities of edge servers necessitate further study on energy-efficient Deep Neural Network (DNN) inference. While availability of DNN model variants enables adaptive selection without compromising accuracy, it increases the complexity of the solution space. Also, existing research on model selection for DNN inference lacks efficient estimation of energy consumption. This paper proposes a polynomial-time joint strategy for QoS-aware model instance provisioning and selection, based on many-to-many stable matching. Our novel formulation uses the number of floating-point operations (FLOPs) of each model along with hardware-level characteristics of edge servers to minimize total energy usage while maximizing successful inference completions. The proposed strategy is evaluated under different preference functions. Experimental results, compared to optimal and evolutionary algorithms, demonstrate the runtime efficiency of our strategy. Furthermore, extensive evaluations against baselines highlights its superior performance and the importance of jointly considering both system- and application-level parameters in the solution.