At the time, Caesar's heir was a position without precedent. Caesar, alongside his peers Pompey and Crassus, had accumulated unprecedented degrees of wealth, power, and clients. The person who inherited Caesar's name inherited the power to move the Roman world, from client kings and ennobled senators down to the lowest rung of society.

It's hard to say with certainty what Caesar had in mind for Octavian's cursus honorum, but given the conventional career Caesar himself enjoyed until his governorship of Gaul, it's perfectly possible that Octavian would have been developed in line with Roman tradition. We know Octavian was in Macedonia for the planned Parthian war, which would mark Octavian as a military tribune, a typical rank for a Roman aristocrat of his age. After that, he likely would have ascended to quaestor, aedile, praetor, and finally consul, each in his proper year.

Even without the blessings of Caesar, Octavian would have had good career prospects. His father won the praetorship, an impressive accomplishment for a novus homo, and was likely very rich; how else would a complete new man have been able to marry Caesar's niece, an offshoot of the celebrated patrician Julii family? When you add that his stepfather was Lucius Marcius Philippus, of an established consular family claiming descent from the King of Rome, his connections and personal fortune were enough on their own to raise his nomen into the rarefied air of Roman nobility.

As we all know, once Caesar died, Octavian made his own career track, but that brings us to the next part of the question: "Why Octavian?"

My colleague /u/XenophonTheAthenian has answered this in other threads, and while I disagree with some of what he writes, the short version is that Mark Antony was supposed to be the original heir, but had thoroughly disappointed and offended Caesar. Caesar used Mark Antony, but never again allowed him free reign. The final choice came down between Decimus Brutus and Gaius Octavius, and for whatever reason, Caesar chose the dark horse, Octavian, as the frontrunner, with the proviso that if Octavian died, Decimus Brutus would be the heir.

As his grand-nephew, Caesar likely would have interacted with the toddler Octavian at family gatherings, but Octavian grew up while Caesar was fighting in Gaul. We know for certain that Octavian impressed Caesar in Spain and that Octavian was in Macedonia on that fateful Ides of March, but we'll never know why Caesar chose Octavian. Gambler's pick, perhaps?