Alright so my understanding is the bigger the bullet & higher the velocity = The deeper the penetration, bigger the exit wound if there is one, more damage to the impact site & blood loss.
Hollow points break apart on impact inside the target while FMJ is a solid piece of metal, this means there is more surrounding tissue damage with the first type.
A lower velocity or smaller round such as .22 has a lower likelihood of being a clean fatal kill in one shot due to it not being able to rip though a body so easily.
With the shotgun you can go with big buckshot, 00 or 000 or a slug round. A slug is one piece while buckshot is loads of metal ball bearings.
The preference for a round that essentially shatters inside the body is extra damage to surrounding areas, more likelihood of hitting surrounding arteries; organs & faster blood loss.
I'd go for the head over heart but your choice, head being just behind the ear & up a bit, temple on side above cheek bone or back of the skull where bone mass is thinner.