Prompt-based methods leverage the knowledge of pre-trained language models (PLMs) trained with a masked language modeling (MLM) objective; however, these methods are sensitive to template, verbalizer, and few-shot instance selection, particularly in cold-start settings with no labeled data. Existing studies overlook the dependency between instances and verbalizers, where instance-label probabilities depend on verbalizer token proximity in the embedding space. To address this, we propose COLDSELECT, a joint verbalizer and instance selection approach that models data diversity. COLDSELECT maps PLM vocabulary and $h_{[MASK]}$ embeddings into a shared space, applying dimensionality reduction and clustering to ensure efficient and diverse selection. By optimizing for minimal uncertainty and maximal diversity, COLDSELECT captures data relationships effectively. Experiments on eight benchmarks demonstrate COLDSELECT's superiority in reducing uncertainty and enhancing generalization, outperforming baselines in verbalizer and few-shot instance selection for cold-start scenarios.