For home defense you would want to get one with a rifled slug barrel. This barrel is shorter making it better to use in and around the inside of your home ( ie: hallways, etc. ) it also puts out a wider " shot spread " with the shorter barrel, which will increase the kill zone of your shot
I'm going to have to take exception with this advice...a rifled slug barrel is suitable for use with sabot slugs in a deer slug gun, not shotshells in a HD weapon. Perhaps you meant rifle
sights? In which case I agree.
As far as a 'kill zone', a shotgun must still be aimed to be effective. Contrary to popular belief, a shotgun blast does not create a wide swath of destruction downrange. And you are still responsible for where every pellet goes, just as you would be with pistol bullets.
Mamabear, there are several criteria for you to evaluate before you can determine which shotgun best suits your needs.
Remington 870 vs. Mossberg 500
The two ubiquitous brands of fighting pump shotguns sold in the U.S. I personally give a slight edge in quality to the Remington, but you would not be under-armed with either. Both have an extensive array of aftermarket accessories available and come in a variety of confgurations from their respective manufacturers.
Configuration
Ideally, a fighting shotgun should have a barrel length of 18-20" and a full stock (forget about pistol-grip only shotguns; you really need to know what you're doing to be effective with those). Rifle sights are nice, but not essential on a weapon that will be fired at living room distances. Extended magazines, sidesaddles and buttcuff ammo carriers are nice but once again, not absolutely essential for a HD gun. I
am in favor of weapon-mounted lights on HD shotguns.
Will this be a dedicated home defense weapon or will it serve double duty as a sporting gun? Some shotguns are sold as kits with multiple barrels for this very purpose.
12 gauge vs. 20 gauge
A 20 gauge would be perfectly adequate for HD use and offers the advantage of reduced recoil; however, the only practical defensive load available in 20 ga. is #3 buckshot. As far as versatility and variety of ammunition available, the 12 gauge wins hands down. And with reduced-recoil buckshot loads, recoil is very manageable.
Buckshot vs. Birdshot
I have heard far too many stories about people surviving shotgun wounds from birdshot (in a variety of situations, not only SD scenarios) to recommend it for home defense use. IMO, the reduced-recoil 00 buckshot loads offered by Federal and others are the way to go. Yes, the risk of penetration of walls with buckshot pellets is greater than with birdshot...but it's also less than the risk of overpenetration by a pistol bullet. Hit what you're aiming at and it won't be an issue.
As far as slugs go, they have their uses...but CQB in a home defense scenario ain't one of 'em.
To give you an idea of what you can do on a budget, here's a picture of my daughter's shotgun. Several years ago I bought her a Remington 870 Youth Model in 20 gauge just for breaking clay pidgeons with for about $200 (they're a little more now). It came with a 21" barrel (not too long for HD use), a reduced-length stock and screw-in choke tubes (Improved Cylinder is the best choke for HD use, IMO). When she moved out, all I added was a 4-shot Sidesaddle, a Wilson/SGT +2 magazine extension and a Hi-Viz fiber optic front sight, turning it into a fairly decent little HD shotgun.