I agree with m700m. The 12 gauge pump
Mossberg 500 Persuader. (Winchester makes the "Defender.")
I prefer the placement of the Mossberg safety, it's ambidexterous and doesn't require you to remove your trigger finger from the triggerguard, same for the slide release. Replace the plastic safety button with a steel one, add a
side saddle for spare ammo, and Bob's your uncle. You can get a magazine that holds eight rounds from the factory. The barrel is 20 inches.
The real clincher for the Mossberg is having the shell lifter in the up position when the bolt is forward. Mossberg is the only shotgun among the big three, Remington, Winchester and Mossberg, that allows you to reload the magazine without running the risk of getting your thumb stuck between the shell lifter and the receiver when your adrenaline is pumping.
The advantage of the Remington is a steel receiver instead of the Mossberg's aluminum receiver. That might make a difference if you are going to carry it in the trunk of your police cruiser for the next decade with a bunch of stuff bouncing all over it. If it's going to wait behind a door in your home, the aluminum frame will last a lifetime. The advantage of the Remington's steel receiver is more than made up for by the Mossberg's advantages in design.
Ammunition...... My preference is
low recoil 00 buckshot. Invest in hands-on competent training. It's important. A shotgun
does not spray a hail of lead that you do not have to aim. You must know how to safely and effectively use the weapon.
The Mossberg 500 is commonly found on pawn shop shelves for under $150 if you are inclined to consider a used gun. Of course, these will usually be a wood stocked 6 round gun with a 28 inch barrel. Buy one with a slick barrel (no rib) and have it
cut down to a 18.5 inch cylinder bore and add a brass bead. If you want a black stock, get some black paint or order a synthetic stock and forend from Midway or Brownells. I like the small "corn cob" forend because it will not interfere with the side saddle.
You can read more that I have written about home defense shotguns
here. A good comparison of the Mossberg 500 and the Remington 870 can be found
here.
Things to avoid: Slings full of shotgun shells, barrels longer than 20 inches, pistol grips, collapsible stocks. I have also found that heat shields are not necessary. The barrel cools off sufficiently while reloading.
I'll move your thread to General Guns.