Biological membranes are essential for the development and survival of organisms. They can be highly complex, usually comprising a variety of lipids, proteins, and other biomolecules organized around a lipid bilayer structure. This complexity makes studying specific features of biological membranes difficult, with many research studies relying on simplified models, such as artificial vesicles or supported lipid bilayers. Here, we search for a minimal, lipid-only model system of the inner membrane. We aim to retain the main lipidomic components in their native ratio while mimicking the membrane's thermal and mechanical properties. Based on previous studies, we identify 18 potential model systems reflecting key aspects of the known lipidomic composition and progressively narrow down our selection based on the systems' phase transition temperature and mechanical properties. We identify three ternary model systems able to form stable bilayers that can be made of the commercially available synthetic lipids 16:0-18:1 phosphatidylethanolamine (POPE), 16:0-18:1 phosphatidylglycerol (POPG), and 16:0-18:1 cardiolipin (CL). We anticipate our results to be of interest for future studies making use of models, for example, investigating membrane proteins' function or macromolecule-membrane interactions.