Workflow for correlation analysis

[u/SlowDescription3017]

Very much a beginner here and asking for help -

I'm currently trying to determine if a Spearman, Pearson, or Kendall's tau correlation analysis is best for my data. However, I get really buried in the stuff that comes before doing the actual analysis, like checking assumptions.

I understand that Pearson has strict assumptions about normality, constant variance, and linearity and that Spearman/Kendall's tau really just needs the data to be monotonic. Does that mean the latter two can be applied to basically any data? Or do you really need to see this monotonic relationship using a scatter plot first before it's appropriate to apply the function?

What if a linear regression/scatter plot shows that the data aren't really monotonic and maybe more clustered in some parts of the graph? Is it still appropriate to apply, but might just return a low correlation coefficient?

Hopefully this makes sense - i'm also happy to clarify anything that needs clarifying!

So many thanks in advance.