Is there a list of the most common Lego Technic parts?
On Brickset, you can browse parts in the technic subcategory and you can  sort by "Set count", i.e. the number of sets the element appears in.

https://brickset.com/parts/category-Technic

So that would take care of your "most common" requirement. I'm afraid that "most important" or "helpful" is rather subjective and hence difficult to quantify and have lists sorted by those measures...