The increasing awareness to maximize the use of energy resources has led to exploration in effective energy storage viz. high energy density batteries which are reliable, cost-effective and have low energy losses. This has spearheaded the development of solid polymer electrolytes for safer lithium-ion batteries with comparable properties to conventional liquid electrolyte-based lithium-ion batteries. Since the polymer functions as the electrolyte as well as the separator, they must possess a number of critical properties to seamlessly function in the battery. The electrochemical stability window (ESW) is a critical consideration which determines the safe operational voltage outside which the electrolyte degrades. Another factor is the Li-binding energy of the ions to the polymer which is a prelude to the Li-ion migration in the electrolyte and provides an estimate of the solubility of the salt in the polymer matrix. An optimal binding energy is desired where it is high enough for the Li-ion to bind to the polymer but not high enough to prevent its migration through the electrolyte. In this work, molecular dynamics (MD) and density functional theory (DFT) calculations are performed to determine the ESW and the binding energy of polyethylene oxide (PEO), an excellent inflammable and stable polymer electrolyte with multiple Li salts namely, LiBr, LiCl, LiI, LiClO₄, LiSCN, LiCH₃COO, LiNO₃, LiBH₄, LiCF₃SO₃ and LiBF₄ to ascertain realistic ESW and binding energy values. We establish a relationship between the effects of the salt anion on the ESW and the binding energy. The ESW decreases in the presence of a salt in the polymer host, and we explore the effects of the salt anion size on the ESW. We also determine an optimal binding energy range for PEO with the salts which successfully propagates polymer-salt solvation as well as Li-ion migration. We believe this study should be able to guide the experimental design of stable and safe solid polymer electrolytes in the future.