Hearts of Stone
Updates from checking errata and the official rules question forum…
You don't need to run/charge the target for a Push or Shield Bash. You just have to move 3" towards the target.
Success on the opposed Strength roll for a Push moves the target back 1". One or more raises moves it back 2". You can't Push a target more than 2" back.
Shield Bash is not an attack, so you can't use the Wild Attack option and there is no additional damage from a raise on the opposed Strength roll. However you do count the +2 damage from drawing a Joker for initiative.
The opposed Strength roll is not used for damage, because it is a Trait roll not a damage roll.
So the best case is: You Shield Bash with a large shield, get a raise on the opposed Strength roll, and the target also hits an obstacle. The target first takes Strength +3 damage from being rammed with a shield, and then takes 2d6 damage from hitting the obstacle. Those are two separate damage rolls.
(You can also use your shield as an Improvised Weapon, in which case you make a Fighting attack at -2 because it's in your off hand.)