Is there a list of the most common Lego Technic parts? I searched the internet for this and I found a list of complete sets. But I am looking for a list of the most common (and in some sense the most important or most helpful) individual Lego Technic parts. Is this available somewhere?
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...