Why should you care about this? Maybe you shouldn't. But when we're trying to figure out just whom the candidates might be in a case like, say,
Missouri, it's helpful to have some notion of how senators get to be where they are. Are we right to focus heavily on members of the Congress? (Yes — this is where an awful lot of Senators come from.) How common is it for someone to be elected to the Senate after having held no previous elected office? (Not very common — but more common than you might think).
Nearly half of the current members of the Senate were members of the U.S. House at some before becoming senators — usually immediately beforehand. A lot of these folks, moreover, were in their state legislatures before becoming representatives. This is the most basic path by which one pursues a political career: State Representative –> State Senator –> U.S. Representative — > U.S. Senator. Especially talented candidates — for example, our President-elect — can and do bypass the stint in the House, but this is still fairly rare, even if it seems to be occurring somewhat more frequently than it once did.
The other major path toward becoming a senator is from the state executive branch. About one quarter of the current population of the Senate held statewide elected office before taking their new jobs, including 11 former elected governors. From among the other statewide offices, attorney generals have been on something of a hot streak of late, presently accounting for 7 seats in the Senate, but there are also state auditors, state treasurers, tax commissioners (Kent Conrad; I'd originally missed the fact that this is an elected office in North Dakota) and lieutenant governors.