The choice of which method to choose for multiple comparisons depends upon you making a judgement as to which is best in your case, and upon some practical considerations, like which method is commonly used in your field.

I know. That's very helpful.

Bonferroni is very conservative.  That is, you are very unlikely to find false differences between groups.  But you are also likely to miss significant differences that you would find with another method.  In my opinion, it is too conservative in most cases.  But again, this is a decision you have to make for your own research.  If it is important to you to not find any false differences, then a conservative method is good for you.  However, if it is more important to not exclude differences that are probably real, then a less-conservative approach is better for you.

My best advice to read about the methods and choose the one you find would be best in your research.

Thanks, Salvatore.

If you have more than 3groups to compare, better analyse the significant differences with DMRT. One post-hoc test would be ideal.

Avoid Bonferroni corrections and the like by not relying on ANOVA because of the inherent difficulties, which Salvatore mentioned. I prefer to use ML to find the most likely distribution of each of your samples (technically more rigorously phrased: the distribution of the population from which the sample(s) have been drawn). Then use a likelihood ratio test (i.e. Wilks lambda) to test whether the two samples could have been drawn from the same distribution. Such a methodology avoids any of the correction quagmires, is clean and rigorous. It also gives you more information about the clutches than means and estimated variances.

Cheers, Hermann