Business, law, entrepreneurship, military service, maybe some politics (but not necessary).
Anything that involves negotiation, public speaking, networking, resilience under scrutiny and criticism, a track record of success, etc.
Your suggestions are right on. Are you aware that many politicians are lawyers. In fact, 51% of U.S. Senators, 30% of the House, and 35% of congress overall have law degrees. Until recently, around two thirds of our Presidents were lawyers prior to becoming President. The numbers are similar for state politicians. Belonging a member of a political party is only a part of being someone political. Political means to be engaged in how a group, community, or society makes decisions, exercises power and distributes resources. Successful politicians should have knowledge of how to pass laws, run campaigns, and manage public policy.
Oregon Labor Candidate School offers instruction on how to become a politician. The program provides instruction on the practical mechanics of running a campaign—including fundraising, targeting voters, crafting an effective message, and building a campaign team. Many politicians begin their political careers by being elected to School Boards and City Councils. One of the first things students learn at Oregon Candidate School is how to effectively raise money to run a political campaign.