Federated learning is an effective method to train a machine learning model without requiring to aggregate the potentially sensitive data of agents in a central server. However, the limited communication bandwidth, the hardware of the agents and a potential application-specific latency requirement impact how many and which agents can participate in the learning process at each communication round. In this paper, we propose a selection metric characterizing each agent’s importance with respect to both the learning process and the resource efficiency of its wireless communication channel. Leveraging this importance metric, we formulate a general agent selection optimization problem, which can be adapted to different environments with latency or resource-oriented constraints. Considering an example wireless environment with latency constraints, the agent selection problem reduces to the 0/1 Knapsack problem, which we solve with a fully polynomial approximation. We then evaluate the agent selection policy in different scenarios, using extensive simulations for an example task of object classification of European traffic signs. The results indicate that agent selection policies which consider both learning and channel aspects provide benefits in terms of the attainable global model accuracy and/or the time needed to achieve a targeted accuracy level. However, in scenarios where agents have a limited number of data samples or where the latency requirement is very stringent, a pure learning-based agent selection policy is shown to be more beneficial during the early or late stages of the learning process.@en