Hi, your 686 is plenty stout for any load you prefer.
Try a bunch of stuff and shoot what your gun "likes" best, accuracy-wise.
That being said, your shooting situation will also dictate what to use.
For home, indoor self-defense in a city setting, I'd want a bullet that wouldn't zip through three walls and take out the wife or a kid. I'd want a round that would not over-penetrate. Frankly, I'd also make that round one of the fine .38 Special loads for this very reason.
For car defense I'd want a bullet that would penetrate like heck in case I had to use it against an attacker shooting at me from a car!
For hunting, I'd want a big azzz (heavy) 180 grain bullet with lots of knock down power that's designed for hunting.
For paper punching you can't beat the single hole potential of the wonderful 148 grain Wadcutter bullets, in either .38 special or .357.
I'd also recommend taking up handloading to save tons of money, and to save all your spent brass. My target loads are light kicking and easy on the guns . . . and super accurate. You'll be amazed at how soon you'll save enough money reloading . . . to buy another gun!!!
Question? What do I keep loaded as a great all-around .357 load in my .357s? The legendary 125 grain Federal HydraShock that has the best one shot stop statistics of any handgun round, in any caliber, in years of documented gun fight data.
BTW, I recommend using only store-bought branded ammo for self-defense purposes, to prevent some attorney from accusing you of "spiking" your handloads to cause his client more suffering. Any of the preferred loads used by law enforcement personnel will thus suffice, but I prefer Federal in my revolvers due to Federal primers being the most reliable in revolvers.
Hope this helps,
T.