The .30-06 will take down anything on this continent, IF you do your part. Your part is to practice, if you don't do that, it really doesn't matter which caliber that you choose.
Lets get somehing a little bit durable. If this is to be used when the "balloon goes up", you can't be running to your local gunsmith twice a month.shame, if $ are limited, to limit yourself to a bolt action. A used, Remington autorifle, in 308, would be far more to the point, since it offers a fast second shot, sometimes useful to anchor a fleeing cripple. Also useful on running coyotes, on dog packs, to stop charges by animals, and for self defense or combat matchs. <$400, used, and sometimes a scope will be part of the deal. 308 milsurp ammo is far cheaper than 3006 for practice, and in reality, a good 308 softpoint, like the Nosler Partition, will do anything that the 3006 can do, game-wise.
many varmints have fallen to .308.remington auto is 2 MOA, and that's deer-capable to 300m, easily, and only slobs try longer ranges. The critter is too likely to move while the bullet's in flight. 308 is not a varmint round, and only varmints require better than 2 MOA accuracy.