From Atkins and Atkins Handbook to Life in Ancient Rome:
"The Senate was a group of unelected men called senators, restricted to patricians in the early republic but later extended to plebeians. In the middle and late republic a man was automatically admitted to the Senate for life once he had been elected by the comitia or concilium to his first magistracy. He was expelled only if found guilty of misconduct."
The Senate was originally an advisory body to the King. In the Republic period, it advised the executive branch, first praetores, and then the consules once the consuls were introduced. Later, it took over supreme power of Rome until the Social Revolution, in which the Senate power was opposed by the Populists, like the Gracchi, who used the position of the Tribunus Plebis to make laws overriding and circumnavigating the Senate.
To be a Senator, you could not own any type of business except agriculture.