Who is the best person to care for my preemie? Resident, fellow, np, neonatologist?

All. Looks like you are in academic center. In the best case scenario all of the professionals you mentioned work as a team and communicate with each other. Many double check points and an opportunity to get different opinions. The neonatologist is the person with more training and (usually) experience but it is important for you to be comfortable to communicate with one or all of them!
Need the best care. Regardless of who you see evaluating your preemie in the intensive care nursery, the plan of medical care lays in the hands of a neonatologist. He or she is ultimately responsible for the preemies as the attending physician, each unit or hospital nicu, have unique methods to render coverage 24/7, university hospitals may have residents and fellows, smaller facilities nnp's and neonatologists.