This paper introduces GestureCoach, a system designed to help speakers deliver more engaging talks by guiding them to gesture effectively during rehearsal. GestureCoach combines an LLM-driven gesture recommendation model with a rehearsal interface that proactively cues speakers to gesture appropriately. Trained on experts' gesturing patterns from TED talks, the model consists of two modules: an emphasis proposal module, which predicts when to gesture by identifying gesture-worthy text segments in the presenter notes, and a gesture identification module, which determines what gesture to use by retrieving semantically appropriate gestures from a curated gesture database. Results of a model performance evaluation and user study (N=30) show that the emphasis proposal module outperforms off-the-shelf LLMs in identifying suitable gesture regions, and that participants rated the majority of these predicted regions and their corresponding gestures as highly appropriate. A subsequent user study (N=10) showed that rehearsing with GestureCoach encouraged speakers to gesture and significantly increased gesture diversity, resulting in more engaging talks. We conclude with design implications for future AI-driven rehearsal systems.