For my two cent's worth (which is only worth a penny anymore), I must also agree with glockman10mm in favoring (a) larger caliber first and (b) a heavier bullet in any caliber as generally being my favorite for stopping people at very close range - and not elephants, rinos, or a pesky bear in a tree stand at a considerable distance.
There are so many different and confusing physics aspects to consider about any particular bullet and the speed at which it's travelling that pertain to the related penetration into a chunk of meat and the force being applied to said chunk of meat while penetration progresses. Depending on the game you're intending to drop and the distance involved, all of those physics factors combine very differently when trying to determine which particular combination of those factors will be most effective for the intended purpose. SD (sectional density) is a very important penetration aspect of bullets having the same cross-sectional diameter (caliber); but there is also the major increase in applied energy being absorbed by the piece of meat (as penetration progresses) that is directly proportional to an increase in the bullet's cross-sectional diameter (CSD) as well. Another frequently overlooked major ingredient to the stew is mass-inertia (MI) of the projectile at any given velocity.
SD has already been very comprehensively covered, so I'll try to quickly brush upon CSD (cross-sectional diameter) and MI (mass inertia) as two other important factors to consider. Granted, the muzzle-energy (or just plain ole energy) can be matched by a lighter projectile running at higher velocity with that of a heavier projectile running at a lower velocity; but simply looking at say 900 ft/lbs of equal energy delivered by two different bullets of different weights and/or diameters is not "equal" in effect by any means whatsoever. "Penetration" makes a hole that severs blood vessels and/or internal organs that will eventually cause the demise of a living target just like an arrow, knife, or ice pick easily do; but without concurrently delivering (and expending) a great amount of energy (force) upon the target, it will either run away to die, chew you to pieces, or empty a magazine in your direction before eventually collapsing. If I should stab and deeply penetrate an attacker with eventually fatal wounds with a knife, arrow, or ice pick, that attacker would still pose a major threat to my life for a considerable length of time. If I should soundly whack an attacker with a baseball bat, he/she would instantly get knocked flat on his/her a$$ and be totally incapacitated (threat stopped) for a considerable length of time even though there was no penetration or an eventually fatal wound inflicted. Why? Because I have delivered (and they have absorbed) an immense amount of shock-force (energy directly expended upon the body) that instantly removed the threat they posed whether a fatal wound was concurrently delivered or not. Remember, self-defense is "stopping the threat" and not necessarily "intending to kill" - stuff that can easily crucify you later in criminal or civil court.
When considereing CSD alone with regard to "equal" muzzle-energy, one could easily drive a .22 bullet fast enough to contain the same energy as a much slower-moving .45ACP bullet (let's say again around 900 ft/lbs). However, the very narrow CSD of even a hollow-point .22 bullet at such high velocity would cause it to completely penetrate and fully exit soft tissue of a human body with the bullet retaining a great amount of its initial energy upon exit; therefore, while a fatal wound may have been created, the body most likely only felt a "sting" because it only absorbed less than 100 ft/lbs of bullet's energy before it exited. However, the .45ACP bullet with a much wider CSD would logarithmically see a much higher resistance to penetration depth while it's slower velocity would also combine to stop the bullet inside the target without exiting; therefore, whatever wound was created is greatly augmented by the "baseball bat" effect of the body absorbing the full 900 ft/lbs of bullet energy.
Even when bullet weight, CSD and SD are relatively equal, the velocity at which the bullet is travelling will also create a major difference in the effectiveness of shock-force (energy absorbed by the target). Anyone who has been in combat, worked an ER, or taken a bullet themselves will quickly attest that a high level of force absorbed by the body (and inernal organs) can be fatal when the wound itself wouldn't have been. Case in point was the "Son of Sam" serial killer from many years ago who walked up to his victims and fired point-blank with a .44 magnum short-barreled revolver using hollow-point bullets. While he killed many people before he was caught, less than half of his victims died as a result of their wound(s) because every shot from the high-velocity .44 mag at such close range (irregardless of the hollow-points) completely penetrated the victims with very little bullet expansion which (in turn) expended very little of the bullet's energy on their body as it quickly passed through. Therefore, the survivors were ones that didn't suffer a fatal penetration wound when there was a minimal shock-force concurrently applied to the body as well. While the facts weren't widely publicized, every law enforcement agency, combat veteran, and medical trauma expert were in total agreement that the death rate (considering the wounds inflicted) would have most likely been over 90% had he been using a much lower-velocity .45ACP that would have added a much higher blunt-force trauma to the physical wound itself.
The MI (mass inertia) factor is easy to visualize by considering if you would rather try using your arm to deflect a soccer ball or a bowling ball that were both coming toward you at the same velocity. Maybe also think about taking a running start to either punt a soccer ball or a bowling ball with all your might. The simple physics definition is that "inertia of motion" means that matter in motion tends to remain in motion, and will offer a restance to its motion being slowed or deflected in another direction with a counter-force that is directly proportional to its mass density (weight/inertia = MI) - which quickly becomes apparent when trying to stop the soccer ball or the bowling ball with your arm (or head). In the same respect, the "inertia of rest" means that matter at rest tends to remain at rest, and will oppose any force trying to put it in motion with a counter-force directly proportional to its mass density (weight/inertia = MI) - which also becomes apparent from the force applied to your toe when punting a soccer ball or a bowling ball.
The MI stuff sounds like mumbo-jumbo to many, but the "inertia of rest" is why your heater has a significantly higher recoil (using the same powder charge) with a heavy bullet than it does with a lighter bullet. In the same respect, the "inertia of motion" is why a light weight bullet (especially at high velocity) is easily deflected off target by nothing more than hitting a fly or tiny twig in its path - while a heavy bullet of lower velocity will bulldoze its way through thick brush to find its intended mark. In bad memory days of stinking Nam jungles, an M-16 on full auto was virtually worthless when shooting through even light cover; and there is personal witness of many instances when (what should have been a fatal shot) was deflected away from internal organs when it hit a rib and took more rounds to finish the job - unfortunatly, not before the target inflicted a casualty of our own on more occasions than I care to remember. In a "heavy cover" close-range firefight, the smart ones were pulling their .45ACP and praying to God that the point and/or drag men were still alive and effectively mowing the lawn with their bootleg Brownings spraying 00-buck into the bush that quickly sent the survivors into disappearance mode.
MI and lower velocity in close-quarter situations definitely have major advantages when conditions are far from being textbook perfect according to all the whoopie high-tech ballastics and modern tactical crap. Consider the fact that far more soldiers have fallen from a primitive, 450-grain, .58 caliber, black powder musket round at close range than from anything that ever came along later. Just food for thought.