When you say self defense are you talking home, CCW, or Open carry?
For CCW a small 9mm or 38 special will work better for most people IMHO.
For Open carry or home defense in a revolver I would probably pick a 44 mag or 44 Special.
The first handgun I owned was a 357. Because that is what
everyone said was the best choice for a beginner. Even though the first handgun I shot was a Colt Delta in 10mm. I shot that 10mm a lot and I liked it but I knew the ammo was to hard to get and spendy for my budget at the time. But looking back I think a 9mm or 45 auto would have been a better first handgun or even a 44 magnum revolver. The 9mm or 45 are much better choices for CCW because they are easier to conceal than a 4" 357. While a 44 mag loaded with a good 44 special HP offers the same ballistics as a 45 acp and mild recoil and blast, but can be loaded up with 44 magnums for hunting or sport.
***
Your asking which cartridge is the better self defense round which isn't exactly the right question. A better question is with what gun/cartridge combination can I become the most skilled. Which is a combination of ergonomics [including decent trigger pull & fit], logistics [the cheaper it is to purchase and feed the more practice is possible for given amount of money], and confidence in the weapon/caliber of choice. If you believe in big slow bullets you would be better off with such, but if you think small & fast is the way to go then you should get that.
Also for CCW you need to consider how easy it will be for you to carry it. Mouse guns have always been very popular because they are easier to carry than a service sized pistol. On the other hand I know people that carry a pair of 45 acps and some that carry 44 mags for CCW on a regular basis.
***
With the 125 JHP full power load the 357 is effective. But the recoil and blast are not fun at all, at least when shot in DA mode from normal 4" guns. Which makes it much more difficult to become skilled in the use of a gun loaded with 357 mag. I have noticed that shooting my 357 in SA mode is more comfortable, probably because I can maintain a better grip.
A 9mm gives up a little in theory to a full powered 357 but is much easier and enjoyable to shoot. And if you us a Glock or other SA type gun the trigger is a lot easier to manage than the DA trigger on most revolvers [a tuned Colt python's DA trigger would probably be much better than a Glock's trigger
]
Picking the gun that "fits" your hand the best and that you have most confidence in is the way to go IMHO.
As to over penetration, remember in real life you will be lucky if 1/2 to 3/4 of your rounds hit the target your aiming at...so the real concern about overpenetration should be for the rounds that miss target completly.