I am not a stranger to handguns, or to military rifles, I qualified expert on both a .45 and an M16,
Okay; so you're familiar with the peephole aperature sights of the M16, and have at least a passing familiarity with or working knowledge of the Kalishnikov AK design, fielded worldwide in at least 100 million examples. That is a lot of rifles, a very major production series of any industrial device ot tool, and an impressive testament to the Kalishnikov design's functionality.
No, probably neither an AK nor the more American opposite number, Stoner's AR 15/ M16, is what you want as a hunting weapon. Instead, consider the previously most successful military weapon fielded before the AK leadspreader came along to take over first place: the Mauser turnbolt rifle; with the model 98 version being the most developed and widely issued.
It was successful enough that after facing Spasnish Mausers during the Spanish-American War, we abandoned the recently introduced Krag-Jorgenson repeater less than a decade old and developed a Mauser copy that served American soldiers well in both the First Great War and the Second. Since you're used to the peephole aperarture sights of an M16, those on an M1903A3 Springfield would likely be familiar to you. The usual; caliber is the .30-06 US government M2 chambering, but alterations are both possible and common.
But it was the *pure* Mauser used by Germany in both wars; and more than half of the nations of the world. A dozen common military chamberings will accomplish the task you describe and have done so for years. At least two dozen less common possibilities also exist, and one of them might work nearly as well for you; maybe even better, and might be the bargain that happens to come your way and can't be denied.
Prices on a used military Mauser model 98 can run you anywhere from $50 or so for a well-used Turkish 8mm to a couple of hundred dollars for a specimin of the WWII German infantryman's karbiner 98 K battle rifle, produced in the millions and of which many survived their wars in varying states of repair. But there's very little that can go wrong with a Mauser bolt-action rifle, and if a part or two is worn or otherwise out of specs, they're not at all hard to work on and get back into top-motch condition.
A few countries or empires developed alternatives to the Mauser bolt gun, and one of them might also do for you. Great Britain's Enfield rifles are a fascinating field of study in and of themselves and can certainly do in this century much of that they did throughout the span of the last one. If virtually limited to the rimmed British .303 service rifle cartridge, at least it's a good one. And there are Enfields in the hands of scared young troops today, serving their nation and the member of that nation who bears that rifle.
Likewise the Russian Mosin-Nagant design served in the hundreds of thousands and can be had very reasonably priced; in this case, the cartridge will almost certainly be the 7.62x54mm rimmed design of 1891 that still serves Russia in the SVD sniper's rifle and PK machineguns. They too can be found in a variety of price ranges and conditions. And Japan offered their Arisaka Mauser copy in two calibers, a 6.5mm and a .30, Switzerland a 7.5mm machine tool that required no turn of the bolt to work, just a pull to the rear followedc by a return push forward. Sweden issued a superbly crafted Mauser of an earlier design in a very efficient 6.5mm chambering, and South and Central America considered a wide spread of mostly Mauser designs in a range of calibers: the 7.65mm version used by Argentina and also Belgium, the 7mm caliber of those early Spanish Mausers that so impressed the Americans facing them, and versions in the same 8mm and .30 calibers the Germans and US used. You could probably make do with any of them. But if you have a choice? Go with the Mauser 98K, in the German Army's chosen configuration. Ammo remains very available for it, and is still in service here and there. If you're so inclined, you can rework the rifle to another caliber if you wear iot out from excessive shooting or neglected maintenance, but the original condition is a good place to start.
Spend as much on ammunition as you do on the rifle, and after that's used up, you'll know enough about what you're doing that it won't matter if some other possible configuration offers a slight improvement. You'll be able to get the job done.
Maybe at that point you may want to fit a telescopic sight to your rifle; or you may not need one by then. That's another consideration and choice to be made farther down that road. But for now, there's a good rifle waiting to meet you.
