Tukey HSD is generally a good option to control the FWER of all-pairwise comparisons, given the assumption of a conditional normal distribution is reasonable.

Use Anova followed by Bonferroni corrections  as this correction is much stringent than Turkey test

From what I read... What? Okay, yes it was Wikipedia... What?  No, I don't usually read up on statistical tests on Wikipedia.... Huh?  Well it sounded reasonable when I read it ...

Anyway, it sounds like Newman - Keuls is more liberal, in the sense that it is more likely to commit so-called type i errors over type ii errors.  Your decision might rest on how you balance this trade-off .

[No Wikipedia articles were harmed in writing of this post.]