I do not think that the .410 is enough gun for defense against anything bigger than rats or snakes. The largest shot size available in .410 is #4 birdshot, which only penetrates approximately 4" in ballistic gelatin--insufficient for reliable stopping power. I personally would not use any shot size smaller than #4 BUCK.
Theoretically, the 16 gauge should work fine for home defense; 16 gauge buckshot is loaded with #1 buck, which is probably the ideal shot size for defensive applications. However, I am not aware of any currently produced 16 gauge pump shotguns (or any other kind for that matter); I do not believe any home defense-oriented shotgun has ever been made in 16 gauge. Sixteen gauge shells are getting a little hard to find, especially buckshot. Bottom line--the 16 would work, but why go through the trouble of getting a shotgun in an obsolete chambering and having to hunt for the shells?
The 20 gauge has some appeal due to its lower recoil. However, with the new reduced recoil buckshot loads (sometimes marketed as "Tactical buckshot"), the 12 gauge is entirely managable. Tactical accessories such as the Sure-Fire flashlight forend, the sidesaddle shell holder, and ghost ring sights are all made only for 12 gauge shotguns (the only combat-type accessories for the 20 gauge are the Choate magazine extensions for the Remington 870 and 1100). Again, the 20 would work, but why bother?
The 12 gauge is by far the best choice for a home defense shotgun.