The best descriptor for goodness of fit is some measure of the divergence between the distribution of residuals of your fit and the distribution of residuals you expect knowing "the statistical characteristics of your measurements". If you for example have normal-distributed measurements with variance 1, you should have residuals with a standard-deviation of 1. This is a necessary condition for a good fit, but since a set of alternating residuals of +1 and -1 will give you a standard deviation of 1 too, it is not a sufficient condition. If you instead look at the distribution of the residuals (histogram or something similar) it should be consistent with comming from a normal-distribution. That was a very birds-eye view of this.
My practical advice is to save away the residuals and then calculate the histograms of their distribution and pick the narrowest one with a "nice shape"...
