Developing efficient on-the-edge Deep Learning (DL) applications is a challenging and non-trivial task, as first different DL models need to be explored with different trade-offs between accuracy and complexity, second, various optimization options, frameworks and libraries are available that need to be explored, third, a wide range of edge devices are available with different computation and memory constraints. As such, trade-offs arise among inference time, energy consumption, efficiency (throughput/watt) and value (throughput/dollar). To shed some light in this problem, a case study is delivered where seven Image Classification (IC) and six Object Detection (OD) State-of-The-Art (SOTA) DL models were used to detect face masks on the following commercial off-the-shelf edge devices: Raspberry PI 4, Intel Neural Compute Stick 2, Jetson Nano, Jetson Xavier NX, and i.MX 8M Plus. First, a full end-to-end video pipeline face mask wearing detection architecture is developed. Then, the thirteen DL models were optimized, evaluated and compared on the edge devices, in terms of accuracy and inference time. To leverage the computational power of the edge devices, the models have been optimized, first, by using the SOTA optimization frameworks (TensorFlow Lite, OpenVINO, TensorRT, eIQ) and, second, by evaluating/comparing different optimization options, e.g., different levels of quantization. Note that the five edge devices are evaluated and compared too, in terms of inference time, value and efficiency. Last, we obtain insightful observations on which optimization frameworks, libraries and options to use and on how to select the right device depending on the target metric (inference time, efficiency and value). For example, we show that Jetson Xavier NX platform is the best in terms of latency and efficiency (FPS/Watt), while Jetson Nano is the best in terms of value (FPS/$).