You don't say if you have a firearms background or if you own any guns. That might be a good place to start. You can learn good field marksmanship techniques in about a week under a good instructor. I state field marksmanship because many who post on here don't seem to know the difference between the shooting one might expect to do at the range; from the bench, on a well defined stationary target, at a measured distance, and shooting in the field where in addition to the challenges of shooting on the range you have to deal with hold the rifle in your hands, and engage a partially obscured target that holds a stationary position only momentarily, has a poorly defined aiming point and is most often observed at an unknown range.
Yet we hear people say they have the best hunting rifle because it shoots into a half minute. In the field reliability, durability, and good handling qualities in your rifle trump any concerns you might have concerning anything greater than what might be consider mundane accuracy. Naturally the farther away you intend to shoot, the greater the need there is for precise accuracy, but over normal hunting ranges which might extend to 300 yards or so, 2-3 MOA is more than sufficient, and more than the vast majority of hunter can hold.
With respect to power, the more powerful your rifle the more difficult it is to shoot due to blast and recoil. I consider the 6.5X55 cartridge to be a good minimum recommendation for all North American big game. The rifles tend to be accurate and reasonably flat shooting and the blast and recoil is easy on the marksman. The cartridge provides a nice balance between the .243 Winchester which isn't quite enough, and the .30/06 which some find a bit much for medium sized game and extended range time.
While many insist a rimfire is the best rifle to learn marksmanship with, I don't believe that to be necessarily true. A centerfire rifle has the benefit of providing an avenue for dry firing without causing damage to the rifle. Much can be gained from dry firing drills at home. Place a quarter on top of the barrel near the muzzle and attempt to dry fire without knocking it off. When you can do this repeatedly you will have mastered the trigger control portion of the marksmanship problem and you'll only have position, breathing, and focus to work on.
