It depends on the configuration of true group means and on the specific post-hoc tests you plan to conduct.

Let's say you are doing a oneway anova with $G$ groups. You can choose between one the following strategies:

1. Perform an overall F-test for differences between the group means.

2. Perform t-tests for all possible pairwise comparisons, with multiple testing adjustment. The overall F-test is more powerful if the true group means are equally spaced. The pairwise t-ests will be more powerful if one or two true means are dramatically different to the others.

Another way to conduct the post-hoc tests it to test each group mean vs the average of the other group means. This approach is more powerful than either of the other approaches for detecting one group separate to the others.

If the anova is balanced (equal numbers in each group) then one can also consider Tukey's honestly significant differences, which is similar to making all possible pairwise comparisons but more powerful because the method accounts for the dependencies between the pairwise comparisons. The rest of my remarks apply to any anova, balanced or otherwise.