Shooting goats/tahr/deer up to about 250-280M is one game that I happily do with just about any rifle scope combination that will hold a reliable zero. Shooting them around 300 starts to get interesting and I like a rifle that will consistently shoot under 1.5 moa - practically any modern centrefire.
Past 350 and it's a different game, and my first thought always is to get closer, which is nearly always possible in any terrain for anyone who has spent a bit of time in the high country and is proficient in reading "the lye of the land". It's more reliable, easier and cheaper to learn to get a bit closer than it is to learn to shoot at long range.
And a rifle to do it then? Well first you're gonna have to get you head around the old adage "spend more money on your scope than your rifle" - the scope is the critical tool.. The rifle under it - just about any modern well tuned factory rifle with careful handloads along with plenty of practice will get you shooting sub MOA and that's good enough think about extending your range past 400M.
Personally, despite frequently shooting my hunting rifles to 600Y on the range, I wouldn't bother trying to shoot a deer past 400M, and that would be in extreme circumstances. Recently I watched one of the best stags I've ever seen from 360M but passed up the shot, just too hard to read what the wind was doing accross the gullies. We stalked in closer but he'd jisted it. Still better that wounding and losing it.
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