Travel to Gunbarrel to meet the man John Marshall in his bar, and accept his quest to rid the sewers of the mutant presence under the town. Most other weapons you can obtain in Rage 2 are all found in Arks that are scattered around the map, but one of them is part of the main story. You technically have three character you need to find and help in the Wasteland, and it might not be clear what awaits you down each path. Get the Combat Shotgun (Story Mission) in Rage 2 You can only buy it from weapon merchants in the Trading Outposts - and they sell BFG Plasma Capsules for $1,000 each! You won't find it out in the wild or at bandit camps.
It's important to note that while deadly - ammo for the BFG is scarce. Look around for an impact site in the hill by the converging roads, and you'll spot a broken red rock that holds the BFG 9000 inside. When leaving Vineland after the tutorial and driving your new Phoenix car, keep a lookout for a falling red meteorite that will hit the ground just past the second three-way intersection to the right and up past Vineland.
Deluxe Edition players get access to the BFG 9000 from Doom, but you have to find it first.