I stand by the Deliverer being the best weapon.
It increases the amount of AP you have in VATS, with some stat points in agility and perception you have lots of AP, plus the AP bonus from the gun, and you have good accuracy in VATS. Get the Sneak perk so you do 2.5x damage (then 3.0x, then 3.5x) while in sneak mode (crouching). Come up behind your enemy quietly or enemies and just take them out easy. I can take out Supermutant Behemoths or Queen Mirelluks in 5 shots doing this, and I can take 20+ shots in a single VATS session before using up all my AP.
It absolutely destroys everything, and it uses 10mm rounds which are cheap and common. Combine with other perks and legendary armour that increases VATS or AP refresh speed etc and you're king of the wasteland. I can just sneak into the middle of an area quietly, hit VATS and cycle through the targets, I'll take out most raiders, supermutants and synths with one bullet each, and because the Deliverer comes with a suppressor (so you don't have to upgrade Gunsmith perk) no one else in the area will hear you and you'll stay hidden.
For supporting weapons I have a kitted out .50 Sniper Rifle, and another Sniper Rifle that uses .38 rounds because .50 aren't so common. Then I also have Kellogs Pistol because it's incredibly powerful and good for close range stuff if I run out of 10mm rounds. And the Les Teribles legendary shotgun for when I need to go gung-ho.