Node classification is an essential problem in graph learning. However, many models typically obtain unsatisfactory performance when applied to few-shot scenarios. Some studies have attempted to combine meta-learning with graph neural networks to solve few-shot node classification on graphs. Despite their promising performance, some limitations remain. First, they employ the node encoding mechanism of homophilic graphs to learn node embeddings, even in heterophilic graphs. Second, existing models based on meta-learning ignore the interference of randomness in the learning process. Third, they are trained using only limited labeled nodes within the specific task, without explicitly utilizing numerous unlabeled nodes. Finally, they treat almost all sampled tasks equally without customizing them for their uniqueness. To address these issues, we propose a novel framework for few-shot node classification called Meta-GPS++. Specifically, we first adopt an efficient method to learn discriminative node representations on homophilic and heterophilic graphs. Then, we leverage a prototype-based approach to initialize parameters and contrastive learning for regularizing the distribution of node embeddings. Moreover, we apply self-training to extract valuable information from unlabeled nodes. Additionally, we adopt S$^2$ (scaling & shifting) transformation to learn transferable knowledge from diverse tasks. The results on real-world datasets show the superiority of Meta-GPS++. Our code is available here.