"IS it saying the guy nominated shall have the qualifications required for nominations of the largest number of incumbents in a branch of the state legislatures?"  I believe the "electors" in each State (that will be electing the US Senator) must have the same qualifications as qualifications needed to hold office in the most numerous branch of the State legislatures, i.e. the State House of Representatives <as you stated. That way, US senators are actually voted for by the people, not by popular vote but rather by the peoples' elected representatives. The most populous branch of the State Government chooses the electors who then elect Ambassadors to the US Senate in DC. Hence, more peoples from the State were involved in electing their US Senator. People elect Rep > Rep elects US Senator > Senator represents State and votes according to how he is instructed by his State's legislature/government. If the Senator goes rogue, he can be immediately recalled and replaced. But I could be completely wrong also.