"Legitimacy" is merely a construct that has applicability only in the legal and social context of a particular period of time. Emperors were raised and killed and damned within months, sometimes weeks. The "Senate" approved or did not get a
choice to approve, or endorsed or withdrew endorsement, based on their perception of their self-interest, the number of Senators who
had not been killed in last month's battle, and
military exigencies. Their endorsement was irrelevant if the closest army was bigger than the second-closest army. A "usurper" was a person who died before commissioning an official
history that survived long enough to be copied and survive to today. A "legitimate" emperor
had better public relations staff. Some of the women on the coins, "
Augusta" or not,
had more influence than the male "
Augustus", and were often the conduit for that
man's "legitimacy".
There's no magic involved, just politics. So, collect the coins that interest you.