The residuals of the models should (preferably) be sampled from a normally distributed population. Not the unconditional values of the dependent variable. Moreover, if the sample is large enough, even non-normal residuals do not compromise the result of the statistical test.

Wilcoxon is no direct alternative to a t-test, since Wilcoxon (for dependent variables which are measured on an ordinal scale) doesn't test for mean differences.

Transformation is sometimes a good idea if there are inherent reasons for it and results are interpretable (e.g. often income, or time-associated variables such as reaction speed etc. could reasonably be logarithmically transformed), but not just for achieving normality.

With kind regards

K.