I do not limit myself to a specific engineering revision of any of the Smith and Wesson Models
There has been a Smith and Wesson J-frame, mostly a 2" Model 60 Chief's Special or 2" Model 60 Chief's Special Target, with me almost every day of my life since 1980
In addition to sometimes doing duty as a backup to a larger handgun, it has performed all of those tasks over the last almost 4 decades
The ammunition choice has changed over time as the strength of the firearms has increased and projectile construction has advanced.
Pretty much any of the hollow point Premium Self Defense loads from the Big ammunition companies will be more than satisfactory for any role except hunting backup.
For hunting backup, presuming you can handle it, a solid hard cast projectile at the highest power level your firearm is safe with.
I would also carry a 3" hunting as opposed to the 2" J-frame, but not every one has access to a 3"
And it depends how dangerous the game is, I might opt in for a larger cartridge
As best as possible you want to use the right tool for the job