Schools of statistical inference

So why writing about statistics, while there is so much about it out there already? It is just the problem... Let alone consider frequentist statistics, it is quite a mess today. Scientific literature combines schools of the previous century such as fixed-level testing (rejection/acceptance of Neyman and Pearson), showing actual p-values (Fisher) and parameters estimation such as maximum likelihood or use of confidence intervals. So how to infer based on your data? Even more what about Bayesians with their subjectivity? What about non-informative priors? And the third school, fiducial inference?

Probably too complicated for the 'everyday' scientist, including myself. So let's see what is what, and try to find the right one, possibly without diving into all those formulas of the macho math gurus.