On the other hand, I've had rifles that would easily shoot sub MOA and they never accomplished anything spectacular at all hunting.
While it is certainly possible to have great results hunting with a rifle that is only capable of "2.25 MOA", anything less than that is an advantage in that it eliminates a little more of one of the variables that go into having a bullet strike closer to where you want it to land, AT ANY RANGE.
I would venture that any time a very accurate rifle fails to accomplish anything "at all spectacular while hunting", it is NOT due to the use of a highly accurate rifle.
However, I do agree that to keep things reasonable, the .243 Win. may be the best choice. Personally, I would use the 6mm Remington, as I consider it a slightly better cartridge design, and since I handload all my ammunition, lack of awide variety of factory loads is of no concern to me at all.
I would avoid things like the .240 Weatherby, as it hasone of those damned (and worthless eye candy) belts on it. If I were to go for a .30/'06-capacity case for the 6mm, I'd choose the 6mm/284. However, as noted above, you do not want a cartridge of such a great powder capacith that it willeat upyour barrel before you find a good load for it!