Tbh, I tried several different functions, but nothing worked better than inverse quadric function. Though, I'm not sure if I tried anything without decay
One interesting group is the compactly supported RBFs, for example those of Wendland https://math.iit.edu/~fass/603_ch4.pdf the advantage being that the resulting linear systems are sparse, useful when you have lots of points to interpolate and "gaps" is not an issue.