quality of fit measure

I have a list of data {x,y,f(x,y)} with f being an experimental number and x and y are parameters of the experiment. I am using NonlinearModelFit to fit a model function to these data, with a fairly wide range of models available.
In order to distinguish between the various model fits I need a simple to use measure for the goodness of fit. I have tried to read through ‘Numerical Operations on Data’, but I am overwhelmed by the discussion there. I also know about the possibility to get more infos on the nonlinear fit from nlm["ParameterTable"] and the such. I am no specialist in statistics; all I need is one number, say the chi-squared per degree of freedom, to have a measure for the goodness of fit. How do I get that? What to use?