Hmmmm. So, at this point, I think at least your contenders are something like:
1) .223/5.56
2) 12 guage
3) .308 - or .30-06. I lump the two of them together as they tend to be very similar cartridges in alot of ways.
More or less if you are going to get out of the .22 caliber it is hard to see any other pistol class caliber being in the top three. Maybe .44 magnum and .357 magnum rounding out the top 5, but again some reasonable competition from something like a .243. Or possibly 7.62x39 or even the venerable 30-30.
So, if you rank them in choices of platform, it's probably something like:
1) .223 - pretty much you can get about anything chambered in this.
2) .308/30-06 - ditto here, AR-10/Benelli M1 to bolt action to single shot
3) 12 guage - again plenty of platforms - but perhaps not necessarily the versatility within platform. For example a short barrel tactical shotgun isn't that great for bird hunting, and probably average for slug based deer hunting. A good hunting shotgun may not be that convenient for other tasks. Still, not much to complain about here.
If you rank them in terms of versatility ...
1) Maybe the .223 - you can get these anywhere from about 40 grains to 73. You can get penetrator, to soft tip to frangible to controlled expansion. It's almost too much for small game, and just barely enough with the right bullet for deer. Most platforms are very manageable in most situations and accurate to several hundred yards with average skill.
2) The .308/30-.06 - I could even concede the argument that this is more versatile except around the management of platforms. The AR-10 is not as handy as an M-4. The M1A1 is not as handy as a Benelli MR-1. Certainly, whatever versatility in loads you can get in .223 you can get in either 30 caliber platform and while it is probably too much for small game (if it's smaller than a cat I'm not sure how much is left to recover for the pot) it's enough to take you up to any North American game animal.
3) The 12 guage is arguably either #3 or number #1. Certainly you can get everything from flare and non - lethal to really hard hitting heavyweight magnum slugs. Of course all sorts of rounds for birds, etc. However, at the end of the day there isn't anything that makes a shotgun a more than 100 yard weapon. Maybe 125 yards. Depending on where in the world you live, that could be a real problem. Further, shortening the barrel of a shotgun has a disproportionate effect on it's versatility in comparison to a rifle.
At the end of the day - personally, I think I look for some kind of higher capacity rig in a semi - auto 30-06 or .308. I'm going to have to assume I can maintain it, one way or another, and there is a narrow defensive scenario where a magazine fed semi - auto is a better choice than box fed bolt action. That probably puts me into one of the lighter weight AR-10 platforms, an FNAR or FN-SCAR platform, a Benelli M-1 or possibly even a Kel-Tec or Browning BAR platform to end on two extremes.
As much as the .223 came out ahead in most categories I tend to think I can load a .30 caliber down with a heavy bullet and manage my defensive scenarios than load it up to get into dealing with larger critters. At least where I live, if I get out into the woods, squirrels and rabbits aren't plentiful enough to cut it, but we have deer, black bear, the occasional moose and elk along with larger predator animals. I know messing with the loads messes with whether I turn my semi - auto into a single shot, but if I'm going to focus on a specific platform I can probably do some work on it to manage that.
Put some good quality variable power glass, back up sights, and if I'm really that concerned about CQB sort of scenarios some kind of co located single lens (but not battery powered!) optic.
It's really a toss up between the three though. Any real change in decision factor (i.e. better portability of weapon and ammo - moves to the .223. More likelihood of need for a closer quarters weapon moves to shotgun) changes the decision.
Which is probably why next to .22 those three are among the most popular platforms and calibers in North America.
Thinkingblade