I don't own a Governor, but I do own Taurus Judge, which is essentially the basis on which the Governor was built.
The Judge primarily serves as my bedside Home Defense firearm, but it's a lot of fun to take out to the range as well.
.45 Long Colt Cowboy Action Loads are the most comfortable to shoot, but .410 Bore shotshells are by far more entertaining to shoot.
When it comes to self-defense, I keep it loaded with 3 rounds of Federal Premium .410 Handgun 000 Buck and 2 rounds of Barnes VOR-TX 200gr .45LC JHPs.
As others have said, you're going to get naysayers who insist that these weapons are novelties/gimmicks with absolutely no practical use, but there are plenty of ammo tests on YouTube which prove otherwise, especially those of Shootingthebull410. The trick it to only use loads which are designed for handguns, as loads designed for full-length shotguns with 18"+ barrels predictably don't perform well out of a 2.5" rifled barrel.
Just be aware that the Judge/Governor are not in the same league as a 12 Gauge shotgun. If a short-barrel pistol grip shotgun is what you desire, then get a Mossberg Shockwave, Remington Tac-14, or Chiappa Hancho.