OK:target,hunting and defense. caliber
You want a target accurate gun.
Second you want a hunting gun. To me that means it has to be capable of mouse to elephant.
Defense?
If it's a hunting gun, and not an autoloader, it can always be loaded down to work for defense.
A target gun needs to be built well, have an inherently accurate cartridge, a fantastic trigger, and great sites.
I have two nominations:
First is the .475 Linebaugh. It's inherently accurate, can be load mouse to elephant, and, in a custom gun built on a Freedom Arms 83 will cloverleaf at 50 yards, with 5 shots.
Next caliber:
.510 Linebaugh Maximum
Can use 525 grain bullets, suitable if you have to worry about the rouge elephant, and, can be loaded down as well. Again, big bullets make for accurate guns.
Either of these guns can be loaded with 260-300 grain Hawk HPS, with thin jackets, that expand very quickly, and, at around 1500-1900 fps give you .357 type ballistics, with a MUCH heavier bullet. Heavy and fast, the way to go for defense. You can also tailor the load to the gun weight, to have it recoil like a 9mm, if you want.