I understand that when performing linear regression, one common rule-of-thumb is that for a good 'fit', the residuals should be 1) independently distributed, 2) stationary and 3) not serially correlated. In practical terms, this can be achieved with multiple statistical tools i.e. Augmented Dickey-Fuller (ADF) a Ljung-Box (lag=1) tests on the residuals.

What is the convention, if any, regarding this type of regression analysis i.e. what are the recommended statistical tests to infer if a model fit is appropriate? For instance, is testing for stationarity strictly required when testing for auto-correlation (as non-stationary trends would exhibit autocorrelation)? Or is just testing the residuals for normality (e.g. with a Kolmogorov-Smirnov test) sufficient?