In the post-Marian army of the Roman Late Republic, there were 80 basic infantry soldiers in a century (ten groups of eight-man tents, and an average of a helper or two mixed per tent). Each century was lead by a centurion, his second (called an optio), and a few other various minor positions which were not really leadership roles (like the century's standard-bearer). So technically the ratio was 80:1 per century. There were six centuries in a cohort, and the centurion of "top" century in each cohort was considered to be senior to the other five and (probably) led the cohort of 480 men at the tactical level. There were ten cohorts in the legion, with the first cohort having five jumbo-sized centuries instead of the regular six. The first century of that first cohort was led by the most senior centurion of the legion, and the other four in the first cohort formed a sort of informal advisory board called the primi ordines ("first ranks"). Sometimes we hear Caesar consulting centurions for key decisions, and he probably means these five. The most senior centurion (of the first century of the first cohort) was called the primus pilus.

Centurions moved up in rank as they did cool stuff or as those above them died, as did soldiers (more rarely). The most senior and promising optio candidates replaced lost centurions. Generally speaking, the legion was constantly filtering itself, with the soldiers who performed well moving up through the ranks towards first century of first cohort, and the same for centurions. Caesar mentions that the centurions were in constant competition with each other, or at least some were. Centurions were drawn from within the infantry ranks, typically--that is, they were non-commissioned officers, and were typically not noble or well-connected. They got their position based on merit, experience, and their popularity among the rank and file. Beyond the centurions, all the rest of the senior leadership were generally there by birth or station, not by merit. There were six tribunes of the soldiers per legion, and by Caesar's time they were appointed by the commander and were generally well-connected men in their late teens just starting on their careers. Though Caesar sometimes consults them, they were not very experienced and were there to learn, not lead, though we do sometimes see them in leadership roles. There was a quaestor usually, but he rarely was asked to lead. The rest of the leadership, besides the (pro)consul or (pro)praetor (ie the commander), were legati. It is a complicated topic, but the legates were appointed by the commander and received imperium from him. They could be anybody, in theory, but were generally there either for political reasons (like Cicero's little brother Quintus) or because they were good at leading (like Labienus or M. Antonius).

SO: in sum, for every legion there were 59 centurions, 59 of their trainees / second in command, six tribunes who would typically not lead or do anything useful, and a legate or commander.

See this old thread, though I admit I'm still not sure on the details of what my interlocutor was saying.