Supervised administration can be described as a series of formal proceedings from beginning to end. Generally, if there is no dispute over the admission of the will and appointment of a personal representative I would begin with informal proceedings. If it is likely that the will may be contested at some point or the appointment of the personal representative contested, I would consider using formal proceedings. There would seem to be very little advantage for requesting supervised administration since you can obtain court orders when necessary by using formal proceedings for a particular issue. An attorney should be consulted and retained to handle the probate proceedings.
Estates are almost always complicated enough to justify such professional services.
My experience as a judge has been that in most cases in which someone tried to probate an estate without legal assistance, it has been a disaster and the decision was regretted.