Self-supervised learning (SSL) has emerged as a powerful framework to learn representations from raw data without supervision. Yet in practice, engineers face issues such as instability in tuning optimizers and collapse of representations during training. Such challenges motivate the need for a theory to shed light on the complex interplay between the choice of data augmentation, network architecture, and training algorithm. % on the resulting performance in downstream tasks. We study such an interplay with a precise analysis of generalization performance on both pretraining and downstream tasks in kernel regimes, and highlight several insights for SSL practitioners that arise from our theory.