In this paper, we present a vision-based model called MRI-CORE, trained on over 110,000 MRI images (over 6 million slices) for 18 body parts to address the data shortage problem in medical image analysis. MRI-CORE demonstrates better performance than state-of-the-art methods on 13 data-constrained segmentation tasks, image classification, and zero-shot segmentation, suggesting its potential to contribute to the development of data-efficient AI models. We also present a strategy for obtaining the most informative base model and a novel analysis of the relationship between the similarity between pretraining and subtask data and transfer learning performance, and the model is publicly available.