The periods 293 through 219 BC and 166 to 9 BC are vague because of missing Livy volumes and lesser (or no) alternative sources for those ranges.
Aside from age, being a (primary major family) Patrician was a factor for some of the Roman Kingdom, at other times the pool expanded to include minor Patrician families. During the Kingdom the Senate largely worked as an advisory council to the king, grinding through legislative details, and more or less being responsible for the election of new kings (variously with or without input from "the people").