Foundation models have revolutionized various fields such as natural language processing (NLP) and computer vision (CV). While efforts have been made to transfer the success of the foundation models in general AI domains to biology, existing works focus on directly adopting the existing foundation model architectures from general machine learning domains without a systematic design considering the unique physicochemical and structural properties of each biological data modality. This leads to suboptimal performance, as these repurposed architectures struggle to capture the long-range dependencies, sparse information, and complex underlying ``grammars'' inherent to biological data. To address this gap, we introduce BioArc, a novel framework designed to move beyond intuition-driven architecture design towards principled, automated architecture discovery for biological foundation models. Leveraging Neural Architecture Search (NAS), BioArc systematically explores a vast architecture design space, evaluating architectures across multiple biological modalities while rigorously analyzing the interplay between architecture, tokenization, and training strategies. This large-scale analysis identifies novel, high-performance architectures, allowing us to distill a set of empirical design principles to guide future model development. Furthermore, to make the best of this set of discovered principled architectures, we propose and compare several architecture prediction methods that effectively and efficiently predict optimal architectures for new biological tasks. Overall, our work provides a foundational resource and a principled methodology to guide the creation of the next generation of task-specific and foundation models for biology.