Choosing the right correlation test for the given variables

Question

I need to choose between Pearson, Spearman and Kendall's tau correlations for the given varibles $A$ and $B$:

1. $A,B$ are continuous with importance to value
2. $A,B$ are ordinal variables
3. $A$ is continuous and $B$ is ordinal
4. $A,B$ are continuous with importance to order

My try:

1. The only correlation test which uses values is Pearson.
2. It seems to me that Kendall's tau best fits though Spearman could be used as well.
3. I've understood that Spearman is good for both continuous and ordinal, but technically we could use Kendall's tau, can't we?
4. Kendall's tau - since the order is important

So as you can see I'm somewhat confused regarding choosing the right test and I'd be glad if you could help me understand what are the appropriate choices.

Thanks