Few shot in-context learning (ICL) typically assumes access to large annotated training sets. However, in many real world scenarios, such as domain adaptation, there is only a limited budget to annotate a small number of samples, with the goal of maximizing downstream performance. We study various methods for selecting samples to annotate within a predefined budget, specifically focusing on the named entity recognition (NER) task, which has real-world applications, is expensive to annotate, and is relatively less studied in ICL setups. Across different models and datasets, we find that a relatively small pool of annotated samples can achieve results comparable to using the entire training set. Moreover, we discover that random selection of samples for annotation yields surprisingly good performance. Finally, we observe that a diverse annotation pool is correlated with improved performance. We hope that future work adopts our realistic paradigm which takes annotation budget into account.