I haven't read through this thread. Not sure if the OP will hand load or not? For all of the bang, recoil and ammo expense I wouldn't touch anything bigger than a 243 for what is contemplated.
Barnes and bonded bullets combined with modern powders have revolutionised the .223. For goats and the odd deer out to 250-300 yards the .223 would fill the bill reasonably cheaply and efficiently I reckon. The kill zone of animal doesn't shrink because you are using a .223. You just need to actually hit.
A 55 grain Barnes TTSX doing 3.2k at the muzzle will go right through a Red at 250 yards, and flatten it.
You can use cheaper bullets than the Barnes on goats, like the Hornady. You just need to fiddle a bit to get the 2 loads in sync.
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