It doesn't really matter what you do, the game will follow the exact same story beats. You can tell the Hardie Boys that you'll side with the tribunal, but you can't. You can become an unwitting pawn to Claire, feeding Joyce information - or not, but the outcome is the same (Joyce leaves, Claire wins). You can never catch the real killer until it's too late, because the game arbitrarily forbids you from exploring every possible point the shot could have originated from. You can not retrieve your gun through any other means that working with Claire - but I suppose it would be foolish for the protagonist to do any detective work in a detective game. You can make a variety of builds, lean into being a cold, soulless logic machine, or a hobo who is attuned to the soul of the city, but then you are railroaded into the Shivers check that mandatorily makes your character a city shaman - again, doing any actual detective work is not an option. You will always get shot in the leg and fall during the Tribunal, which is why the armored pants don't exist in the game - because then you wouldn't be shot.
Do I need to keep going?
There is one sole thing that matters in DE, and it's whether or not you make the Authority check during the tribunal - the ending can be slightly different depending on whether you succeed or fail. Everything else is just an illusion of choice.