Shotguns vs. Chainguns, eh?
Shotguns are 6d3, which means their damage ranges from 6-18 hps worth of damage (let's just say that this is near-kill damage for most early enemies and a nice chunk for later ones); however, this damage decreases over range, so a shot that would have done 18 hps of damage up close only does about 5 when fired at something 7-8 tiles away. If you can afford to get within medium/short/melee range and are sure you can shoot/reload/shoot again/etc. without taking a lot of damage, they can work very well, but if not, they will cause you a lot of frustration (and deaths). I don't usually use shotguns, but if you're going to use them you'll probably want to get a double shotgun as soon as you can find one (since as the name suggests it has two barrels to shoot two spreads for 6d3x2 damage, translating to 12-36 hps worth of damage), especially when you hit the late game with caves of Arachs and Arch-Viles (both of which are rather healthy and will take several shots even at close range, and which can really tear you up if you take too long to kill them; the Arch-Vile may not show/may only show up 3-4 times if you pick ITYTD, but even so he is the worst normal enemy in the normal game cycle you can come across, and the Arach's plasma rifle-esque weapon is no picnic either [and those WILL show up in ITYTD for sure, in numbers]). I also think you might have to take another weapon as well for the times when you need something dead but can't afford it health-wise to get closer; the shotgun doesn't do much good at long-range and some of the tougher monsters can easily fry you while you're on your way over.
Chainguns are 1d6x5, which means that their damage ranges from 5-30 hps worth of damage. This is IMO the easier of the two to work with, since as long as you have some EE and plenty of ammo they can be very, very potent against early and mid-game enemies. Reloader can help here too, since the chaingun has a long reload time. Be forewarned, however, that each bullet gets damage taken off seperately when fired against an enemy wearing armor/that possesses natural armor. If you shoot a human commando and hit with every bullet and he survives, it's because he's got 2 points of armor and 20 hps, and you didn't get all your bullets to do 6 hps of damage (6 x 5 = 30, 6 - 2 = 4, 4 x 5 = 20). Son of a Bitch (which makes you do one hp worth of damage more per bullet) can be a good idea here though, as this not only will compensate for armor but also help to seriously tear up non-armored/under-armored enemies (5-30 hp + 1 SoB = 10-35 hps; +2 SoB = 15-40 hps; +3 SoB = 20-45 hps). Of course, the downside of taking SoB is that you won't be able to take things like Ironman, Hellrunner, or Finesse, which can more directly raise your chances of survival/killing them before they can kill you. One last thing: If you go the chaingun route, you will also want to have a plasma rifle on hand, as it does 1d8x8 damage (8-64 hps of damage) and can be overcharged to fire all 40 shots at once (which is only something you do when you find a second plasma rifle, but which when done will let you seriously harm things like Arachs and Hell Barons within the same timeframe as a normal blast). In fact, the SoB trait is even more useful with the plasma rifle than it is with the chaingun (since instead of adding 5 hps of damage per level, it adds 8 [16-72, 24-80, and 32-88 respective to each level of SoB]).
In the end, it does depend on how you want to play. I don't go with shotguns usually because my playstyle is to avoid blow-for-blow confrontations whenever possible and that's nearly impossible to do well with shotguns (AFAIK at least, if you've got some mad strat then I'd like to hear it). With chainguns and plasma rifles (even with pistols) you can go just out of the line of sight and still get the same level of damage that you would have if you'd shot them from one tile away, and to me that works nicely since then the enemy starts the battle at a disadvantage (at least, it will when better AI is implemented; at the moment the enemies can sadly get so distracted that you can kill them from out of the line of sight without them even moving [under the right conditions anyway.. >_>]) and I can save medkits/armor strength for another battle. But I know that shotguns are a cool item anyway and that it is possible to use them well, so I have no reason to say that chainguns are necessarily better than shotguns.