Regulus/Jamie
We haven't touched Ministry structure because it changes every other day.
If we go by the old system, the Wizengamot needs to nominate him, but that wasn't followed for Harry. Also I'm the Wizengamot at the moment, since I haven't seen Granger.
I'd say let people nominate themselves and vote. It's the only thing possible at this point. The problem is that I don't really see anyone with the connections to get people to listen, not once your father goes rogue as history has proven he does. Really, Theo could not just keep his mouth shut.