The federal office with the oldest minimum age for candidates standing for that position is which of the following selections?

Well, let's review the minimum age for candidacy for elected offices on the federal level:

For US House of Representatives, minimum age is set in the Constitution at 25.
For US Senate, minimum age is 30.
For President of the United States, minimum age is 35.

States have their own rules, and not all states are the same.  Some allow state representatives as young as 18.  In about half the states it's 21.  Some have state representatives' minimum age set at 25 (same as federal statute).
 For governor, most states require a minimum age of 30.