Information Criteria is a more modern selection measure. Measures such as AIC and BIC, attempt to balance fit and complexity
Measures of error (MSE, MAE, RMSE), or a measure of the overall variability in the model, can also be used as a goodness of fit criteria
R-squared is the classic evaluation metric in linear regression, or more precisely if there are multiple predictors, adjusted R-squared.
Global F test is the most high-level model significance measure, which simply reports if any component of the model is significant.