The rapid evolution of Smart Grids (SGs) has improved efficiency, reliability, and sustainability, but also exposed critical infrastructures to sophisticated cyber threats, particularly from emerging quantum computing capabilities. Cryptography is a fundamental tool for securing communication networks, ensuring confidentiality, integrity, and authenticity of data transmission. Public Key Cryptography (PKC), a widely used conventional cryptographic scheme forming the backbone of SG security, facing risks from quantum attacks, necessitating Post-Quantum Cryptography (PQC) adoption. However, resource constraints in SG devices limit broad PQC deployment due to high computational and energy demands. This paper introduces a vulnerability-based optimization framework for selective deployment of quantum-secured links under budget and energy constraint. The proposed method prioritizes communications links based on novel composite vulnerability metrics, ensuring that cryptographic resources are allocated where they provide maximum security impact. By integrating security, cost-efficiency, and energy considerations into the selection strategy, the framework enhances resilience against both classical and quantum-enabled adversaries. The Most Vulnerable First (MVF) approach ranks and secures critical links, maximizing security impact while preserving energy efficiency. Simulation results demonstrate that the proposed approach achieves up to 97.8% security impact against coordinated group attacks, significantly outperforming conventional single-metric, random, or sequential augmentation approaches, while maintaining sustainable operational efficiency. This approach balances enhanced cyber resilience with sustainable operational costs, offering a practical, scalable path toward quantum-secured SG communications.