As has been said...
Remington and Mossberg are basically your two big choices in this area. There are some other contenders, but from what I understand, none compete in the areas of price, quality and pleased customers. Both offer fairly inexpensive shotguns ($300-400 range) shotguns in synthetic or other colors, removable barrels that accept chokes. I just picked up an 870 magnum for about $300-something. I would tend AWAY from automatics for a number of reasons (the biggest one being price and general coolness. You want your gun to be cool, right?)
Ignore all the frills and so on. When you go shopping you'll want a few things:
1) Size - most important. Fire a shotgun, get someone who knows what he's talking about to help you figure out what's comfortable, make sure you have good stance and so on. For men this is a LOT easier than for women. I'm pretty sure this is a conspiracy, as women are scary enough when not armed. If you have to pay an extra $100 for a properly sized gun, pay $100 and get a properly sized gun. Make sure you can comfortably handle the gauge as well. A shotgun is not a lot of use if you haven't spent the time practicing with it, and you won't practice with it if it's not comfortable to shoot. I decided against a 12 gauge in favor of 20 because both my wife and I can fire it more comfortably. Remember, you'll be better with a .22 you've trained with than an assault rifle you've barely taken out of the box. Related, also determine if you're left or right dominant.
2) Mossberg vs. Remington - 80% of shotgun fans say Remington, but they've had market share for a lot longer. If you ask Dave up there, he'll tell you that a thousand years in the future when archeologists are digging up our graves, they'll shake the dust off Remingtons and they'll be ready for shoot, whereas the Mossbergs will need a proper oiling first. Either way, they are quality shotguns and you are unlikely to hit the end of their usable life before you hit the end of your usable life. Worry more about which is more comfortable. Mossberg's tang safety is easier for lefties but neither is a big problem. I personally prefer(red?) Mossbergs, but when I went to the store they had a Remington that fit and no Mossbergs in sight, so I got the Remington. Don't sweat it much either way, it's a question of preference, just understand that whichever one you train with you will be stuck with FOREVER because untraining is impossible! Hahahaha!!
3) Pistol grip only vs. not pistol grip only - Not pistol grip only, end of story. I've had two salesmen try and sell me the pistol grip only version. Unless you are filming a movie, you want a stock (the exception is if you're buying a separate stock to add on yourself). Stock + pistol grip is acceptable.
4) Price - pretty obvious. Shop around, some stores will sell for less than others. The prices stores get is based largely on volume of sales, so more popular stores selling more popular brands will likely charge less. If you see what you want at Wal-Mart for $100 less than it is at the local gun shop, go ahead and pick it up (although for any less I'd get it at the local gun shop. Those guys are on your side in ways Wal-Mart isn't, so it's worth it to keep them in business.) Since your requirements are pretty straightforward, assuming you don't have special size requirements, you may want to consider picking up a gun used. My local store sells used and new, so you can try both out and examine them before you buy.
You will notice, I did not include doodads. The stud sight and lack of a heat shield should be fine for what you're doing. I know that stuff looks really, really cool, but it won't help you. Save the money and spend it on range fees. Should (heaven forbid) clay pigeons ever break into your house, it'll be your practice, not the heat shield, which will determine if you hit or miss.
dedicated trap gun. 