It is hard to give rules of thumb on how to select the best RBF, as the best choice is highly data-dependent. The best guideline is to try all of them with both top-level algorithms (TrialWidths and WidPerDim) and with a sensible number of centers, compare the PRESS/GCV values, then focus on the ones that look most hopeful.
If multiquadrics and thin-plate splines give poor results, it is worth trying them in combination with low-order polynomials as a hybrid spline. Try supplementing multiquadrics with a constant term and thin-plate splines with linear (order 1) terms. See Hybrid Radial Basis Functions.
Watch out for conditioning problems with Gaussian kernels (say condition number > 10^8).
Watch out for strange results with Wendland's functions when the ratio of the number of parameters to the number of observations is high. When these functions have a very small width, each basis function only contributes to the fit at one data point. This is because its support only encompasses the one basis function that is its center. The residuals will be zero at each of the data points chosen as a center, and large at the other data points. This scenario can indicate good RMSE values, but the predictive quality of the network will be poor.
