First-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation for the exchange-correlation functional is crucial, as it strongly affects the accuracy of DFT calculations. This study compares the performance capabilities of three approximations on the energetics, mechanical and electronic properties, and crystal structure of NaAlP₂O₇, which is an insulator with a wide band gap that suppresses its electronic conductivity. Two of these approximations are based on Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) and the other on the strongly constrained and appropriately normed (SCAN) meta-GGA. We explore these materials as a contribution to the development of new solid electrolytes (SEs) for sodium-ion batteries (NIBs), which have the potential to mitigate challenges related to lifecycle, safety, and low ionic conductivity. The performance of these batteries largely emanates from the extraordinary demand for high-performing energy storage technologies. This study revealed that PBEsol accurately predicted lattice parameters that closely aligned with experimental values. However, r2SCAN provided the most reliable predictions of the structural and electronic properties of the NaAlP₂O₇ solid electrolyte compared to PBE and PBEsol. Findings demonstrated that the material is structurally, mechanically, electronically, and thermodynamically stable, but exhibits vibrational instability, which may scatter ions and reduce ionic conductivity due to the presence of imaginary frequencies. Our results highlight the importance of selecting appropriate functionals for solid electrolyte DFT computations. The r2SCAN functional appears to be a promising choice for calculating NaAlP₂O₇ properties.