The rapid transition toward electrified mobility and climate neutrality has prioritized the structural and environmental optimization of battery electric vehicle (BEV) subsystems. While vehicle lightweighting enhances operational efficiency, the production phase of structural enclosures and battery cells frequently introduces severe environmental and economic impacts and supply chain vulnerabilities. This study presents a comprehensive cradle-to-gate environmental Life Cycle Assessment (LCA), Life Cycle Costing (LCC), and semi-quantitative social assessment of alternative battery housing materials and battery cell architectures. To achieve a functionally accurate comparison, alternative materials, including a novel recyclable thermoplastic acrylic sheet molding compound (SMC), commercial thermoset SMCs, aluminum (AlMg3), and stainless steel, are evaluated using an analytical stiffness- and strength-equivalent methodology across three real-world geometric demonstrators. Simultaneously, lithium iron phosphate (LFP) liquid electrolyte prismatic cells and solid-state polymer pouch cells are assessed. Material-level results indicate that while aluminum minimizes structural mass, primary aluminum manufacturing exhibits the highest global warming potential and processing costs. Conversely, Polytec SMC and Elium SMC achieve the lowest environmental impacts alongside with competitive total production costs. At the cell level, prismatic LFP architectures display superior environmental performance compared to solid-state pouch cells, which suffer from the energy-intensive processing and lower volumetric capacity normalization. Demonstrator-level aggregation reveals that the electrochemical cells heavily dominate the environmental and economic footprint of the complete assembly, with the housing accounting for less than 5% of total global warming potential (GWP) and 1% of total costs. The social assessment reveals moderate and comparable performance across all systems, with slight advantages for thermoplastic composite-based configurations in terms of circularity potential and innovation perception. Overall, the study highlights the critical importance of cell architecture and manufacturing processes in determining battery system sustainability, while demonstrating the relevance of lightweight composite housings for reducing structural mass with minimal environmental penalty.