the Julio-Claudians weren't true dynastic divine right rulers in the medieval or early modern sense.

This is important because they didn't have established rules like primogeniture or anything. Augustus was adopted, Tiberius was adopted, Germanicus was presumed heir apparent but died. It wasn't supposed to be a monarchy, there was no set formula for succession.

'The Succession Problem' was always a problem. As Augustus you could select a Caesar who was supposed to succeed you (usually your son, of course, even if your son was Commodus) but as often the army would just acclaim whoever they wanted. Diocletian was trying to codify this with the tetrarchy but it didn't really work because Constantine killed everybody.