Well, Five, I'm a newbie to shotguns, too, and I'm looking for a HD shotgun for the same purposes. Saw your thread on the break-in--thank God they got the bastard. Here's what I've found so far (keep in mind I'm a newbie who doesn't yet own a shotgun).
The research I've done says that pumps used to be much more reliable than early semi-autos, but that the difference in reliability is minimal now. That said, pumps are cheaper.
In general, you want a 12 gauge shotgun with an 18" or 20" barrel with a reasonable magazine capacity. There are several options, from what I've found. I'll go ahead and assume you want a pump to save money and have a nice HD weapon ASAP for your family.
Remington 870 and Mossberg 500 or 590 are excellent pump shotguns, from what I've read on here and elsewhere. Both can be had for a reasonable price new, but a great price used.
The Remington is more expensive, but some argue it has a smoother action. The Mossberg has an ambidextrous safety that some view as better, and it's cheaper and comes with more accessories/well equipped out of the box than the Remington. Both have a wealth of aftermarket parts available (stocks, forends, sights, etc.). I've seen new Mossbergs for around $250 and new Remingtons for $300. Used, people have reported paying less than $100 for a Mossberg 500 at a pawn shop.
Another, and cheaper yet, option is the Maverick 88. Maverick is owned by Mossberg, but it's assembled with less expensive parts (possibly Mexican made). They are rumored to have good reliability and can use Mossberg barrels. They can be had with a large magazine capacity (7+1, I think), and they cost about $100 new in box. It seems the people on here are big fans of them for the money.
As far as new vs. used, I've found that used shotguns are a good place to start since the above mentioned models (Remington and Mossberg) have service lives of hundreds of thousands of rounds and replacement parts are readily available.
Where to buy: I'd start at pawn shops, from what people have said. I located one around here that sells guns (not all of them do around here), and the guy told me he has 20 or 30 Mossbergs and Remingtons. Call pawn shops in your area (they're usually in the shady parts of town around here).
Pistol grip vs. stock: Go with a full stock as people have said the pistol grip only option is hard to hit the broad side of a barn with and difficult to control. Having handled both, I totally agree that the full stock just points better and is easier to control.
Hope that helps.... (from my EXTREMELY limited knowledge since I just started inquiring into shotguns). Try using the advanced search option and look for threads started by "Dave McCracken" with "101" in the title. He's outstandingly helpful.
