The accuracy of separable strategies for constructing full-dimensional potential energy surfaces for collisional energy transfer and collision rate calculations is studied systematically for three alcohols (A = methanol, ethanol, and butanol) and three bath gases (M = Ar, N-2, and H2O). The fitting efficiency (defined as the number of ab initio data required to achieve parametrizations of a desired accuracy) is quantified for both pairwise (Buckingham or "exp6") and nonpairwise (permutationally invariant polynomials, PIPs, of Morse variables) functional forms, for four sampling strategies, and as a function of the complexity and anisotropy of the interaction potential. We find that convergence with respect to the number of sampled ab initio data is largely independent of the choice of functional form but instead varies nearly linearly with the number of adjustable parameters and depends strongly on the sampling strategy. Specifically, the use of biased Sobol quasirandom sampling is similar to 7X more efficient than using unbiased pseudorandom sampling, on average, requiring just similar to 3 computed ab initio energies per adjustable fitting parameter. The pairwise exp6 functional form is shown to provide accurate and transferable parametrizations for M = Ar but is unable to accurately describe alcohol interactions with M = N-2 and H2O. The nonpairwise PIP functional form, which is systematically improvable, can produce separable parametrizations with arbitrarily small fitting errors. However, these can suffer from overfitting, which is demonstrated using dynamics calculations of collision parameters for a large number of exp6 and PIP parametrizations. The tests described here validate a robust strategy for automatically generating A + M potential energy surfaces with minimal human intervention, including a quantifiable out of sample metric for judging the accuracy of the fitted surface. We further analyze this set of automatically generated potential energy surfaces to identify areas where more sophisticated fitting strategies may be desired, including pruning of the PIP expansions for large systems and improved sampling strategies more closely coupled with the description of the functional form.