One of the key things is to be proficient with your weapon. You need to be able to rely on your ability to function with the weapon before you choose to handle it in an emergency. Training and practice is the key.
Practice with what ever you can afford, shoot a lot. Shoot in different conditions. Be really comfortable with the pistol.
Then? About any .38+p or .357 commercial round is going to be pretty dadgum effective should you be unfortunate enough to have to use it. Pick one that is identified as Self Defense or Home Defense.
This is the best advice you can get on this topic:
Use the ammo you can shoot best with and then practice under less than perfect conditions.
Do you have a place you can shoot with the lights out, or in darkness, or while holding a flashlight?
Where your friend can squirt you with a water pistol while you shoot (don't laugh until you've tried it)?
We used to put a square of cardboard inside a tire and roll it to practice on moving targets.
As others here have said, any worthwhile ammo will penetrate interior walls. Most will not go far if they have already passed through part of a human body. People are concerned about overpenetration when they should really be concerned about missing the target.
The Empire State Building shooting is a perfect, bad example. Every one of the nine (yes, nine!) innocent people wounded were hit by police gunfire and I'll bet you a donut that none of those bullets went through the criminal first. One of the cops is seen shooting one handed while on the move.
Graphic video shows police killing ESB gunman - CBS News Video
There have been a couple mentions of the 110gr. 357 Magnum load. This ammunition is deliberately downloaded to about 1300 fps as a low recoil alternative to full power .357 loads and is more powerful than any 9mm standard or +p load in this bullet weight. At that speed the bullets will always expand in flesh and are light enough that drywall and studs will tear them up.
I am also a huge fan of the"FBI Load", or as we called it here the Miami Load. This is the 158 grain all lead semi-wadcutter hollowpoint at about 900fps.
In the 70's and into the 90's most departments in South Florida as well as the Federals issued that as service ammunition and they shot a lot of people with it. It works as advertised. I don't remember reading a lot of news stories about criminals wounded by police, but there were a lot of dead ones.
The Remington version of this load has the softest bullet and the largest hollowpoint. The Winchester version is right behind it. In your 686 it's a pussycat, but with teeth.
So, learn to shoot well, practice under poor conditions and have a plan for you and your family. Most likely any shooting will be inside your home, in the wee hours, involving only you, your family and the criminals. A bullet that escapes your home isn't likely to do much harm.
You will probably not be unleashing bullets on a crowded street, but if you carry concealed and that might be a possibility you owe it to everyone around you to be very proficient with your weapon.
Last, consider that you may have to shoot through doors or dryall to get to the bad guy. Once you start shooting they may seek cover as well. Look around your house to see what a Bad Guy could hide behind. Can your bullets penetrate it and still be effective?
For excellent, real world testing on topics like this, I reccommend this site:
The Box O' Truth - The Box O' Truth
This guy shoots everything you can think of into the Box O' Truth, and also the Buick O' Truth. Time spent on this site is time well spent.