Critical questions (CQs) generation for argumentative texts is a key task to promote critical thinking and counter misinformation. In this paper, we present a two-step approach for CQs generation that i) uses a large language model (LLM) for generating candidate CQs, and ii) leverages a fine-tuned classifier for ranking and selecting the top-k most useful CQs to present to the user. We show that such usefulness-based CQs selection consistently improves the performance over the standard application of LLMs. Our system was designed in the context of a shared task on CQs generation hosted at the 12th Workshop on Argument Mining, and represents a viable approach to encourage future developments on CQs generation. Our code is made available to the research community.