Go to a pawn shop or used gun store and find a well functioning Remington 870 pump action, in 12 gauge. Should be no more than $250. It doesn't matter how crappy the stock looks, or even if it's broken. You're going to replace it. Just take it home, clean it up, do these five things to it, and you've got a beast ready to rock the zombies for under $600.
1 - Change the barrel. Unless your pawn shop buy was a tactical model (in which case why are you reading this?), then you'll need to install an 18" cylinder bore barrel, for maximum short range shot spread and ease of maneuvering in tight quarters. $110 from Cheaper Than Dirt and others. http://www.cheaperthandirt.com/product/7-R4620#
2 - Extend the magazine. A "plus two" extension will give you seven in the tube. Many are available at varying prices, but these from TacStar are tried and true, for reasonable dough. $40 from CTD. http://www.cheaperthandirt.com/product/31983
3 - Reduce the recoil. You're a tough guy, sure. But who needs recoil in a rapid-fire situation? Quicken your follow-up shots, make the gun easier for the recoil sensitive to handle, and make it shorter or longer to fit whoever needs to use it, all with this one accessory. The Phoenix Technologies Kicklite Recoil Reducing Tactical Stock. Much more than a butt-pad, this will make shooting comfortable, for $100 or less. I personally wouldn't bother changing the forestock, but it comes with it for the price. http://www.cheaperthandirt.com/product/82583#
4 - Add a light. There are too many ways to go with light selection here, so I'm just going to tell you the best bang for your buck that I've found, for a shotgun, at the moment. This is all about doing tactical for cheaper, right? This actually requires two "parts," but I'm listing them together. Try a simple clamp mount like the TacStar Universal Mount for $16 and the grippy-skinned Streamlight Scorpion X C4 LED, with 200 lumens of blinding, room illuminating power that won't slip out of the clamp after a tube of buckshot, because it's covered with soft rubber. And at $45, it's a hell of a deal.
5 - Add a sling. Don't drop your gun in the middle of a firefight, and don't leave it behind if you need to scoop up the kids and run out the door! A good solid two-point shotgun sling just makes sense. Get one. This one from Blackhawk for $14 also carries 15 extra shells for you. http://www.cheaperthandirt.com/product/8-BH-43SS15BK