Added a stage list. Discuss.
As for selecting the stage, ideally it would be random for first match and then the loser of the previous match selects the next stage. But apparently the only option for stage select in SSBU is having both players choose and then select randomly from those. Having both players select the random stage doesn't really work as there isn't an option to verify that the selected stage actually was randomly selected.
So for the first match we can either select a neutral starting stage that is used in all sets, which both players then select. Alternatively I can randomly select a stage for each matchup. As for the followup matches, the losing player needs to inform the other player on their choice (via the game's voice chat or through other means) so that both players can select the stage.
Or we can come up with some other solution. Unless I'm overthinking this whole thing?