Personal opinion here is that anything much under .17 cal.
does not have a whole lot of serious hunting applications.
That said though, ANY cartridge is fun to shoot!!!!
The smallest bore I have seen is a 2.7 MM.
It was a tiny Semi-auto pistol called a COLIBRI.
and the guy only had about ten rounds for it.
I have a custom built .17 caliber Muzzle loading carbine.
(Fires lead BB's) WHY ? you ask,--- I have no Idea!
It simply seemed like a neat thing to build at the time!