Let’s keep building on what out there for fighters, paladins, and rangers.
Sword and Shield
Once per turn you are wielding both a shield and a one-handed weapon, choose one of the following: Get a +1 bonus to AC, +1 bonus to attack rolls, or reroll once this turn any weapon damage dice that are a 1 keeping the second result.
Thoughts?
Throat Punch Games 
There is already a fighting style like that and fighting with a shield already gives a +2 to AC; why add more? Seems redundant.