I am quite familiar with Roman history, but despite a great wealth of books and podcasts, I have never found a clear explanation of how a roman citizen became a senator. In Latin class I learned about the elaborate system of election used for the magistries in the republican era, and for a long time I believed that membership of the senate was a benefit conferred on those who held senior magistries. But I think that is actually wrong, particulary since the size of the Senate was generally fixed. I've also often seen references to the "Senatorial Class", in a way that implies that it is a separate group to the actual senators and it's membership is defined by property. I understand that the senate's nature, power, size and composition changed dramatically over the course of the republican era and the principate, but no one ever seems to explain how a citizen actually became a senator.
A Roman was appointed to the Senate.
In the early Republic, Consuls held the power to appoint senators. The Plebiscitum Ovinium in about 318 BCE gave that power of senatorial appointment to the Censors. Dictators Sulla and Caesar would exercise the power and similarly the Emperors would in the Empire.
How did a Roman get appointed to the Senate?
Rome had two classes of citizen, Patricians and Plebeians. The reason for the division is not clear but Patrician families may have been wealthy or high status in the Kingdom of Rome period before the Republic and then it became a hereditary family status.
In the early Republic, to become a Senator a man had to be the head of a Patrician family or to have served as an elected magistrate (which were limited to Patricians).
Over time, the Plebeian families were able to gain social and economic power. This lead to demands for political power in what we call the Conflict of the Orders.
The net result was that Plebeians were over a 200 year period increasingly given equal political rights to Patricians.
That meant in theory that any Plebeian could be a magistrate or be appointed to be a Senator.
In practice it was a privilege limited to the richest and most high status Plebeians.
Essentially it seems like the Republic began with a small group of wealthy families called Patricaians who monopolised political power. As time passed some Patricians became poor and some Plebeian families became rich. This lead to new rules on who could hold political power but the intention was the same: limit political power to the richest citizens.
Post Script
It may have been the case that a particularly wealthy Pleb could become a Senator in the early Republic but not passed it to his heir.