We need to move away from the first past the post plurality voting system. We ought to use Range Voting for the president, and use reweighted range voting to select legislators from multimember districts. Ballot access should require submitting an essay explaining the candidate's platform and qualifications, perhaps accompanies by a sworn affidavit so that prevarication becomes criminal perjury. These should be made public in time for vetting, and available for voters to review in the ballot booth.
I would quite like to see the candidates compete against each other on game shows, but who wins according to the rules of the game should not legally determine who wins the office. I'd like to see the candidates compete against each other on both Jeopardy (to show their knowledge) and Family Feud (to show how familiar they are with the concerns of the citizens polled). I really don't see any value in an candidate version of Wheel of Fortune.
There should be more debates in general, including some without any moderators.
Nothing should be determined by physical combat.