Having used the 12.7mm Pistol extensively I would recommend
against it as it lacks punch for its caliber. Instead I would go for the Hunting Revolver, which can be gotten fairly early on in Freeside. You'll need to kill Orris to get it, but he's expendable anyway as
Spoiler he gets removed at the end of the first mission in G. I. Blues if you expose his shenanigans.
Just make sure you're doing that quest and have the info you need, as killing him otherwise will turn Freeside hostile and fail the quest.
True, .45-70 Gov't ammo is not exactly common, but between Gun Runners and the Khans' Armorer you'll have all of them you could ever need and with the Hand-Loader perk you can make the SWC variant which is ridiculously powerful. This weapon does have a goodly STR requirement, unlike most pistols, but it's worth it.
For a shotgun I'd say either the Hunting Shotgun/Dinner Bell (unique variant) or the Riot Gun are the one(s) you want to work toward, and after use of the latter I'd have to say the former might actually be better despite the smaller magazine, as it can be improved through mods while the Riot Gun cannot. They're actually something of a tradeoff, as a modded-out Hunting Shotgun can be used as a ranged weapon while the Riot Gun is devastating at point-blank. Since both use 12ga. ammo you could carry both and not have to worry about swapping ammo types, and eschew an actual rifle-type weapon unless you need something to snipe with.