I'd start with a good lever action. I'd go with a Marlin Cowboy in .44 magnum or .45-70 or possibly the Guide Gun in .45-70. Those choices all attach the magazine to the barrel with a hanger rather than a barrel band which I've found to be more accurate. The rifles are for short to medium range hunting in cover. They are also good for hitting things real hard if you need to. I'd want a light sporter in something between .270 and '06, long action or short. That does almost all of everything else.
The third gun is a puzzle. It may not be needed in most cases. It depends on what you hunt, where your focus is. I would consider an AR-15. With a fast twist and heavy bullets, it'll kill deer. My Ruger MPR will keep 5 70 grain accubonds inside 3/4ths of an inch at 100 yards. Holes frequently touch when I'm shooting the 60 grain Nosler ballistic tip factory load. It is .. flexible. I'd consider a muzzleloader if only because some hunts legally require it. My favorite remains the old TC Big Boar in .58. I regret selling mine. If you hunt long range a lot, then maybe a very large 7mm, .30, or .338 is called for. The only one I've messed with is the STW. If money weren't a consideration, I'd also look at a .338-.378 in the Weatherby Accumark. Something throwing very heavy bullets fast and far for elk .. or anything smaller. I suppose the final consideration would be a .375 H&H. Nostalgia, I guess.
Tom
Anyone who thinks there's two sides to everything hasn't met a M�bius strip.
