For Hand Cannons grab any Jakobs pistol. Irons are the best you’ll come across for a while. But if you can find or grind a Maggie that’d also be a great pick, might have accuracy issues if you don’t have any skills or gear to boost it. The Luck Cannon is your optimal choice but it’s very rare and only found in the dlc.
Anything with a Quad Barrel is your go to very-close-range shotgun, Jakobs and Torgue in particular. But if you want one in a specific element the other manufacturers do fine. Triples barrels aren’t quite as good as Quads but they’ll be more common. Double Barrels might be longer range than you want but they’re usually a great pick too. The Flayer is a really powerful shotgun, but only found in the dlc and is also pretty hard to find, kind of like the Luck Cannon. You’ll get the Boganella off a side mission around level 16 on your first playthrough, it’s no Flayer, but it’s still pretty good and can come in elements. Definitely grab that.
Jack is pretty much always a great pick for your character no matter what build you’re aiming for. But classes are a lot more flexible in this game. Athena might not be a great choice because she’s very elemental dependent which you won’t get on a lot of the best guns for this build. Nisha has some nice synergy with low mag and Non-Elemental weapons that cover all the Jakobs gear you’ll probably end up using, but she might not be accurate in the sense you want her to be(Aimbot action skill).