Out of all of the possible shotgun choices for home defense, one couldn't be better equipped than with the Remington 870. However, I'd like to add a few things.
You can find new and used 870's all day long at just about any gun show. Try to stay with the 870 Express Magnum in 12 guage, therefore you can use 2 3/4 or 3 inch shells. The Express Magnum comes stock with a matte finish (similar to parkerized), satin oiled walnut stock and forearm, and usually a 28" vent rib barrel with choke tubes. A piece fitting this description can be found for as little as $200 (but more likely between $225 - $300 at most shows).
Once you have acquired this beauty, you'll need to dress it up a bit for your specific purpose of home defense. This is why it is preferred to buy a used one. Firstly, and most importantly, get a magazine extension so your shotgun can hold as many as 7-8 rounds. These can be found through catalog houses like "Cheaper Than Dirt" (CTD) for about $30. Next and second in importance is to fit it with the shortest barrel you can find over 18". Remington makes several Express Magnum improved cylinder barrels in this short dimension for around $75-$100 (have seen them at gun shows for $75). Then get yourself a pistol grip to replace your stock (about $16 at CTD). You can also get a pistol grip forearm (also $16 at CTD). If you've gone this far, go ahead and get a barrel clamp with sling swivels ($5)(this allows your magazine extension to be clamped tightly against your barrel) and a sling.
You can also get a BeamShot laser ($80) for your new piece with a push button mounted on the front pistol grip. Now, load it up with OO or OOO buckshot in either 2 3/4 or 3 inch shells and you'll not only be ready for the bad guys, the look of your new doodad alone will scare them silly!!!
A close 2nd choice is the Remington 1100 or 11-87, doing similar modifications as above, except the stock (which cannot be shortened or replaced with just a pistol grip). This is a semi-automatic and is very easy to operate with one hand.