As far as I'm concerned, the Hunting Shotgun is the best close-range vanilla gun in the game. At a minimum you'll want to get the long tube mod for it to increase its ammo capacity. Take the Shotgun Surgeon perk and you can do significant damage even against most armored opponents.
The Assault Carbine works very well too, especially against fast, low DT enemies (cazadors).
ETA - Just wanted to add that, for the range between the shotguns and the sniper rifles, you'll never go wrong with a scoped Trail Carbine.
Hunting shotgun with relevent perks is my new favorite weapon. I do prefer assault carbines (specifically All-American) for mid-range, I don't like the Trail Carbine too much on my current playthrough, more suits the brush gun.
Every gun has its owner, depends a ton on perks you've choosen and your S.P.E.C.I.A.L.
Side-arms are usually a toss up, I have Lucky, Gloria, and Ranger Sequoia to filter through, whichever has the most abundant ammunition.
I will say though, with as much punch as the 12.7mm machine gun packs, I STILL prefer the AA. I suppose its the semi-auto and scope options.