Which Bundren's narrative is the most crucial one in the novel?

This is a tough question because each narrator's contribution is essential to the themes and style of the novel as a whole. Let's consider the few most likely options, though.
Darl Bundren is considered by many to be the central voice of the novel. He narrates more chapters than anyone else and seems to have extrasensory powers. For example, he narrates Addie's death scene even though he and Jewel are away from home. Darl has a more traditional narrative voice since he sounds more intellectual and poetic, whereas the other family members sound like poor country folks with little education. Darl is, for some time, a sort of "voice of reason," and even his act of burning the barn to end the travesty of the journey to Jefferson can be understood by the reader. However, the family commits Darl to a mental hospital since they cannot afford to replace the property Darl destroyed. Darl then seems to have a psychotic break. His character ends up severely damaged by the events of the book.
After Darl is committed, Cash Bundren becomes the voice of reason and the mouthpiece of the idea that sanity and insanity are merely concepts determined by society, not absolutes. Cash is a strong, silent type, and the family relies on his work for their livelihood; this is why they must save his tools when they try to cross the river and things go so terribly wrong. Early in the novel, Cash is only focused on building his mother's coffin, so his chapters are very mechanical; later, he becomes more philosophical, though in a humble way.
Finally, Addie Bundred's chapter must be mentioned. It is the centerpiece (literally) of the novel and provides perspective on the other characters and her relationship with them. Her hatred for most of her family adds a layer of irony and also highlights how selfish each character is in this quest for Jefferson. Also, her comments on language and its inadequacies crystallize an important theme about how useless verbal communication really can be.
Of course, Anse, Dewey Dell, and Vardman also contribute to the novel, and the book would be different without their unique perspectives. In terms of heavy narrative lifting, Darl may be the most significant, but Addie may be even more important in terms of developing Faulkner's central themes.