I did not think about all of that. I feel ill prepared to discuss any of it.
Alan:
URIT gave you some great advice; read Mas Ayoob's books (or better yet, attend his MAG-20 class) about shooting aftermaths and you will learn more.
Home defense is almost always 10 yards or less.... the max straight line distance inside your home. It will be VERY hard to legally justify killing somebody OUTSIDE your dwelling. That is called "hunting" and you aren't a cop chasing a bad guy... you're a civilian, not legally entitles to chase a bad guy outside your home.
The legal cost of a homicide trial (and self defense is still homicide, just justified) to include expert witnesses, ballistics expert, bail, psychologist evaluations, loss of wages, etc.,etc. is well over $100,000, and probably closer to $200,000.
The recoil of a 12 ga with a pistol or bird's head grip is much worse than with a full size stock, even with a 20 ga it is noticeable.
There are only two 12 ga shotguns I would recommend: Mossberg 590A1, or Beretta 1301 Tactical (generation 2). The first is a pump, the second is a semi-auto; both are utterly reliable. There are other acceptable models, but in 12 games these are the two best. (If you are wealthy, you could also get the Benelli M4). For 20 ga the Remington 870, Mossberg 500, Mossberg Maverick are also good.
Always use ammo in either 00 Buck or, preferably in #1 Buck. #4 Buck is acceptable, but only inside a house, which you WILL be staying in (see above), and only if you are proficient with a shotgun. Remember, you ARE responsible for every single pellet, and if you miss the bad guy and hit your wife or kid you are in very deep trouble because you can't claim it is an accident.
Do not use any of the other gimmicky ammo like Dragon's Breath or rubber bullets, etc. ALWAYS use a cylinder bore choke.
Always have a light attached to the shotgun with a momentary on/off switch, preferably by Streamlight, Olight, or Surefire. A light with a green laser is even better.
Barrel should be as short as legally possible to move around corners, that means 18".
Take a "home defense with a shotgun" course and practice reloading... a lot, even though you will probably never have to reload in a real home defense situation, as one well placed 12 or 20 ga hit to the torso is usually an instant stop.
Good luck.