When I go for a dedicated shotgun build (a la AoSg) I generally strive to have a Combat and Double Shotgun in my hands. The Combat will hopefully get turned into a Tactical Shotgun, and the Double is my psuedo-melee option. However, getting that Combat Shotty is far from guaranteed, so I'd suggest getting really comfortable with a vanilla Shotgun.
Some specific builds that I've had success with:
*Pulled off a Quartermaster Gold with a Shottyhead build. That master gives you Juggler and builds easily into Whizkid or Dodgemaster. Because of the hilariously low firetime for Shottyheads, you should definitely try to get an automatic shotgun of some sort. Specifically, you'll want to try and assemble a Tactical Shotgun, or pray for an Assault Shotgun, Plasma Shotgun or maybe even the Jackhammer.
*Fireangel was good until the current version broke its functionality. I'd avoid that trait for now.
*Army of the Dead is a time-tested classic, but I've been taking it somewhat less frequently as of late. Blocking Finesse and Hellrunner is pretty harsh, but it's hard to argue with Piercing damage on all your shotguns.
*For a masterless build, you'll obviously want Shottyman. Anything else is up to you, but I'd suggest getting any of the following: Badass, Dodgemaster, Whizkid, Intuition (Scouts only) or Juggler. As always, Ironman can keep you alive during the brutal lower levels, and a couple extra points of damage from Son of a Bitch will never go unappreciated - it REALLY helps get those "extended"-range kills.
Some basic tactical guidelines:
*Learn to use the vanilla Shotgun. It is absolutely a viable weapon, if a bit awkward, should you never find a Combat Shotgun (which is a very real and disappointing possibility). Regular Shotguns become quite usable with Shottyman and an understanding of cornershooting.
*Cornershooting. Learn it, use it, love it, abuse it. This is the real reason why shotgun builds work. It's a lot of hassle and it requires some patience, but cornershooting is the linchpin that holds shotgun builds together, especially early game. The enemy AI has been modified to be a bit more aggressive. If you hit a monster outside of LOS (say, shooting around a suspicious corner) keep shooting! But listen as well, or maybe wait a couple turns. Try to hear just how many monsters cry out in pain, and also how loud the cries are. With a little practice, you'll have a "player Intuition" that gives you almost as much information as the trait. Best place to practice is in Hell's Arena.
*Shottyman: Know when to reload, know when to move. The thing you need to remember about Shottyman is that your base reload time is probably still a lot less than your movement time. In my book, running-and-gunning against powerful enemies is a "shit just hit the fan" tactic. The best way to avoid damage is to avoid even being targeted by monsters in the first place. Cornershooting works a lot better with a low reload time, as it makes a "knockback lock" much easier to achieve on powerful foes. As a general rule, if you don't need to move during a firefight, you probably should reload while standing still.
*Double Shotgun: The range is really short (8 squares), but the maximum damage is very high up close. I typically use an unmodded Double Shotty as a sort of "shotgunner melee" attack. If you've taken at least 1 level in Whizkid, consider putting together a Focused Double Shotgun, which will grant your weapon the same spread as a basic Shotgun. For a Double Shotty, this dramatically increases the range and effective damage.
As a side note, the rare shotguns can cause ridiculous amounts of carnage when used under a dedicated shotgun build. I've been dying to make a Plasmatic Assault Shotgun under a Shottyhead build one of these days, but I've never had the fortune. The three basic shotguns can do all the damage you need, provided you use them smartly. Well... unless you get a scumbag Former or Baron who snatches up anti-shrapnel armor. Not much you can do there without switching to another weapon class altogether.