If you want a shotgun as soon as possible, then wait to get your weapon back from Lucas. You've got psi, so go do Retake the Outposts and Hopper Round-up using just psi. 0-skill Temporal Distortion and TK Punch will be enough to get you through most of that, so even if you didn't plan on taking Psychokinesis or Temporal Manipulation, you'd still be able to sail through those starting quests. Then, at character level 3 (which might just be after Retaking the Outposts) you should have enough Persuasion (which you'll get by puling 40 points out of Stealth, which that build is overinvested in by a lot) to get the Shoddy Shotty and be ready to go with your shotgun. You can pick up an AR whenever you want; even at level 1 it's possible if you buy two or three grenades. Just head down into the Underpassages, manually engage turn-based mode so you can skirt the Lurker pair and run past the sledge dude, then kill the guy with the aluminized tac vest (if you picked up TD, may as well kill those rathounds and get the loot from inside that locked room, too), open the gate, and kill the Lurker with the AR.
Presto, AR and shotgun by the time you're done with Retaking the Outposts, or Hopper Roundup at the latest.
