To overcome the limitations of long latency and privacy concerns from cloud computing, edge computing along with distributed machine learning such as federated learning (FL), has gained much attention and popularity in academia and industry. Most existing work on FL over the edge mainly focuses on optimizing the training of one shared global model in edge systems. However, with the increasing applications of FL in edge systems, there could be multiple FL models from different applications concurrently being trained in the shared edge cloud. Such concurrent training of these FL models can lead to edge resource competition (for both computing and network resources), and further affect the FL training performance of each other. Therefore, in this paper, considering a multi-model FL scenario, we formulate a joint participant selection and learning optimization problem in a shared edge cloud. This joint optimization aims to determine FL participants and the learning schedule for each FL model such that the total training cost of all FL models in the edge cloud is minimized. We propose a multi-stage optimization framework by decoupling the original problem into two or three subproblems that can be solved respectively and iteratively. Extensive evaluation has been conducted with real-world FL datasets and models. The results have shown that our proposed algorithms can reduce the total cost efficiently compared with prior algorithms.