TL/DR:
My choice for most ideal (defined by me as most versatile or best all around) is the .44mag, even though I don't have one. However, my favorites (in order) are .41mag and .45LC.
My considerations:
I don't handgun hunt, so my big bore needs are fun at the range, self-defense, and for the unlikely event that I may need it for wildlife defense. I live on the East Coast, so I only have to worry about black bear, and most are man-sized (not to mention, bear attacks are quite rare). While a bigger and heavier bullet, and more importantly, more penetration is welcome if I'm ever facing down a big bruin (or perhaps with a higher likelihood, a moose), a large magnum revolver isn't likely needed (well, maybe for moose, but I don't often go far enough north to be in their range). Any non-bear wildlife needs in North America (other than moose) could be covered by any handgun powerful enough for self defense against the criminal element.
That said, I have three contenders for best, one I own, one I used to own, one I probably should own. For range fun, I want manageable recoil while being strong enough to be fun. For self defense, I want something effective with good modern defensive loads easily accessible. Of course, full power is the game in this territory, so something for "bear defense" or similar needs/wants is also on the list of wants. For other considerations, I want easy to find ammo (I do reload to keep ammo costs down, but it isn't an enjoyable hobby in its own right for me, so I do often buy factory ammo), reloading components should be easy to find, and guns in various sizes to cover different needs should be available.
.41mag
My favorite in this category is the .41mag, but it probably isn't "ideal" based on my criteria. It is fun to shoot, it isn't punishing to shoot but has plenty of power (when compared to handguns). However, it suffers quite a bit in gun and ammo availability. It has always been hard to find any ammo in it, and it may not have as many choices in modern defensive rounds as the others. There really aren't many guns made for it, though on the used market there is everything from smallish and concealable (the Taurus 415 on their "compact" frame and the Tracker were both made in .41mag at one time) to full sized and heavy woods guns.
.45LC
My second favorite is .45LC. I love my S&W 625MG. These can be quite mild to shoot, especially with a cowboy loading (store bought or reloads), self defense oriented ammo isn't too hard to find, and you have good woods loads both for "weaker" guns through the Ruger only loadings provided by some specialty companies that are easily up there in heavy .44mag territory. These are the historical choice as well. Pretty much every "cowboy action" SA revolver is made in this caliber, Taurus did make the 450 and Tracker for a truly concealable option (for a few years) and there is the Charter Arms Bulldog XL available in .45LC, while S&W and Ruger make some terrific large frame revolver choices in this caliber. Under normal conditions, you will find the ammo at pretty much any gun shop or outdoors store, but there is a chance that all you'll see are cowboy action loads and maybe one or two defensive choices. These days, you'll probably find something at a gun shop, but you may have few choices. Reloading isn't bad, but the thinner rim does make it a little more tricky than the other two options on my list.
.44mag
I really should have gone with a .44mag as you can't get more versatile (and thus, while not my favorite in this category, in the "real world" it probably is the "ideal" for this need). Like .357mag revolvers and .38spl, you can shoot .44spl loadings for lower recoil practice and fun at the range, and you can have some quite stout magnums when the need (or desire) calls for it. You can load .44mag to stop pretty much anything in North America that you may need to stop. For concealment (and only considering magnum chamberings), Taurus makes the Tracker in .44mag (I haven't looked at their website, if they don't anymore, it was recent), and S&W makes the 69. A little large, but doable. If you are willing to count .44spl in the versatility (since magnums can use their ammo, when looking at the range of available guns that can use the same ammo, I think it is fair), you have the smaller Charter Arms Bulldog, and the discontinued Taurus 445 (but for Taurus non-core offerings, it had a fairly long production run). Still in .44spl, Taurus and Rossi offered K-frame sized options until the 90s or early 2000s (the Taurus 431 and 441 and Rossi 720) and S&W made a variety of options in the L-frame (including quite carryable alloy versions). If you want a SA revolver, the original Ruger Vaquero was made in .44mag (if you can find one) and of course, quite a few options are available in .44spl. Of course, there are plenty of full sized guns available in .44mag with both steel full weight options for recoil control and lighter alloy for carry. Under normal conditions, you'll find a pretty full range of .44mag ammo (and .44spl) in any gun store or outdoor shop, and even today you'll likely have a few options. That last part alone makes this likely the best choice for an "ideal" big bore by itself, and add in the wide variety of guns available and it is the clear winner.
