While admittedly there weren't many other options for someone without an army under their control in a time when the law had become something of a joke I'm curious what Cicero's end goal was with Octavian. Even early on he had shown himself quite willing to ignore the law and the Senate's authority to strengthen his own position and while Antony was certainly the bigger threat to that authority at the time it can't have gone unnoticed that Octavian's actions weren't those of a staunch Republican.
So was Cicero simply doing his best with a bad situation, hoping that once Antony's power was curtailed that Octavian's ambitions could also be dampened and some kind of order restored with the Senate resuming its former prominence? Or did he underestimate just how high Octavian's ambition stretched and really thought he would be the man to restore the Republic?
Unfortunately, our best potential source for this question is lost. Cicero and Octavius (later Octavianus) maintained a lengthy correspondence from 44 BCE all the way down to the former's death, but none of it survives (or at least has not been found). Cicero probably hoped that such a relationship would go roughly like a traditional political apprenticeship, like he had maintained with M. Caelius Rufus. In such relationships, the senior member took the role of a mentor and educator, and Cicero might have thought he could steer the very young Octavius onto some sort of tolerable path. After all, the Optimates had done something similar with the incorrigible Pompey, who was also very young when he showed up on Sulla's doorstep with a private army several decades earlier. He was also ambitious, wild, and dangerous, like a wolf pup. Cicero would not have been blind to the similarities.
If he hoped to control and coerce Octavian with his aged wisdom, he was unsuccessful. Initially, Octavius must have certainly seemed like the lesser of the two evils. Cicero positively despised Antonius, and had hated him for years before the assassination in 44 BCE. Even back in 49 BCE, during the Civil War, Antonius had written nasty letters to Cicero, and by Fall of 44 he could no longer contain himself. This is when we get the Philippic speeches, in which he absolutely lambasts Antonius. From that point on, Cicero would have grasped at just about any option as long as it was not-Antonius. He became positively obsessed with destroying Antonius, and in fact his personal letters become all but exclusively related to this end. Virtually all other gossip and literary chat disappears. Cicero was no fool and he knew that Octavian was going along the same path as his predecessor Julius Caesar, but by the late 40s the remnants of the "senate" had very few realistic options left.