The predictive simulation of molecular liquids requires potential energy surface (PES) models that are not only accurate but also computationally efficient enough to handle the large systems and long time scales required for reliable prediction of macroscopic properties. We present a new approach to the systematic approximation of the first-principles PES of molecular liquids using the GAP (Gaussian Approximation Potential) framework. The approach allows us to create potentials at several different levels of accuracy in reproducing the true PES and thus to determine the level of quantum chemistry that is necessary to accurately predict macroscopic properties. We test the approach by building a series of many-body potentials for liquid methane (CH4), which is difficult to model from first principles because its behavior is dominated by weak dispersion interactions with a significant many-body component. The increasing accuracy of the potentials in predicting the bulk density correlates with their fidelity to the true PES, whereas the trend with the empirical potentials tested is surprisingly the opposite. We conclude that an accurate, consistent prediction of its bulk density across wide ranges of temperature and pressure requires not only many-body dispersion but also quantum nuclear effects to be modeled accurately.