I'm asking a very general question from a position of ignorance: After the second triumvirate, did a Roman emperor with any longevity and/or administrative success ever come out of the Roman Senate? I.e., did a Senator, or even a lower-tier bureaucrat ever rally legions or veterans to his cause, take the purple, and hold it? Or am I misunderstanding in thinking that having the loyalty of legions was even necessary to achieve such an end?
I'm aware of the Praetorian Guard eventually just auctioning off the emperorship during the later years of the Western Empire, but my understanding is ost of them came to ugly ends rather quickly.
Probably the best example I have of this would be Emperor Vespasian. Vespasian was the first emperor of the equestrian class and first in his family to rise to the rank of senator. There he distinguished himself in command through the invasion of Britain and in suppressing a Jewish rebellion in 66 CE.
While Vespasian was besieging Jerusalem, the Emperor Nero had died and kicked off a civil war known as the Year of the Four Emperors which eventually ended with Vespasian's legions hailing him as Imperator and him defeating the Emperor Vitellius.
The next day, he was proclaimed Emperor by the Senate in 69 CE and started a 10 year reign and the next Roman dynasty, the Flavian dynasty. Though there is little account of his government that we have available, we do know that he reformed the Roman financial system and initiated the construction of several projects such as the Flavian Amphitheatre, now known as the the Roman Colosseum.
There are a few others such as Nerva or Septimius Severus who had varying success in there reign but Vespasian does seem to fit the bill best with regards to your question.