Lol at the "Obviously you're going to carry all 3 for the extra/different ammo types". My OCD will allow me to use one item per inventory slot and sell (or stash, provided we have some kind of storage) everything else. Those 2 things will be an LMG and Rocket Launcher. Or one of the other explosive things that I havn't found and tried yet.
Magnum knock back pistol combine with the Intimidation perk near BLur +75% dmg against knocked back, knocked down or flinching. I haven't try it yet, but imagine it will be good.
But autoshotgun is the strongest close quarter, I like the one that shoot nades. SMG burn up ammo which better use for LMG and Pistol is good for headshot.