I remember Mel Tappan doing an article about this sort of thing. And he concluded that a .308 was the way to go. With the smaller diameter bores, it is much tougher to load them down with lead bullets and pistol powder. With a .308 you have basically anything covered as far as big game. Especially with today's modern bullets. But you can also load it with standard lead bullets, patched lead bullets, and even round balls with very small amounts of pistol powder. Very, very versatile.
My "perfect rifle" for this would be a full stock older model Sako rifle. Short and handy and accurate.
You could actually buy a new one...
For that amount of money... I think I would rather buy an older Sako action and have a custom rifle built. That new one is pretty though!