What shot to use is mostly a function of where you live, and what you (Realistically) expect to be facing.
If you live in the country well away from neighbors, #00 would be good.
If you live in an apartment #4 would be a better choice, with some people telling you that even that is too large in a thin-walled apartment.
What you might face also dictates shot size. If you're looking at a car load of bad guys, #00. If you might face a home intruder at 20 feet, #4.
In any event, 3" shells are a case of too much for home defense. Too much recoil, and too much muzzle blast.
In any home defense situation, standard load shells are plenty effective, and are easier to handle in recoil.
The reason the shotgun is the premier HD gun, is SPEED.
The speed at which you can engage a target with a devastating load of shot.
Anything that slows you down reduces the gun's effectiveness, so any accessories you might add or the use of Magnum shells has to be subjected to a "cost/benefit" analysis.
Does the benefit outweigh the reduction in speed?
In the case of Magnum loads, you aren't getting any more "power" as in a Magnum rifle or pistol round, just more shot in the air.
This comes at the "cost" of increased recoil and muzzle blast, and a corresponding decrease of the speed at which you can operate the gun and engage targets.
In any case, Magnum shells are of little actual benefit in a true Home Defense gun situation. While it's nice to have a dense cloud of #00 Magnum buck flying at the bad guy, your neighbors, (and the local District Attorney) might have a few complaints about the load of shot blowing through their wall and hitting someone.
Best advice: Do a "real world" look at your living arrangements and threat situation, then pick the appropriate size shot in a standard load.
Stay away from the "blow the barn door down" loads, and the tricked out "Hollywood Special" guns.