Federated Learning (FL) is an emerging machine learning paradigm that enables the collaborative training of a shared global model across distributed clients while keeping the data decentralized. Recent works on designing systems for efficient FL have shown that utilizing serverless computing technologies, particularly Function-as-a-Service (FaaS) for FL, can enhance resource efficiency, reduce training costs, and alleviate the complex infrastructure management burden on data holders. However, current serverless FL systems still suffer from the presence of stragglers, i.e., slow clients that impede the collaborative training process. While strategies aimed at mitigating stragglers in these systems have been proposed, they overlook the diverse hardware resource configurations among FL clients. To this end, we present Apodotiko, a novel asynchronous training strategy designed for serverless FL. Our strategy incorporates a scoring mechanism that evaluates each client's hardware capacity and dataset size to intelligently prioritize and select clients for each training round, thereby minimizing the effects of stragglers on system performance. We comprehensively evaluate Apodotiko across diverse datasets, considering a mix of CPU and GPU clients, and compare its performance against five other FL training strategies. Results from our experiments demonstrate that Apodotiko outperforms other FL training strategies, achieving an average speedup of 2.75x and a maximum speedup of 7.03x. Furthermore, our strategy significantly reduces cold starts by a factor of four on average, demonstrating suitability in serverless environments.