All of the .30 caliber cartridges you mention have excellent pedigrees in the game fields, and none of them could be considered a poor choice. I don't know you, so I can't say with any certainty what your level of recoil tolerance might be; people, even those with little shooting experience, react to recoil very differently. Muzzle blast can be controlled with hearing protection, and the number of hunters who employ hearing protection in the field is growing. If you shoot factory ammo only, recoil can be mitigated slightly by choosing lighter bullets, but its not enough to help if you're upset by .300 magnum recoil. The only way to know if you can handle a .300 magnum is to shoot a .300 magnum. That said, given the range you intend to shoot from, and the game you intend to shoot, a .300 magnum is a bit much, particularly if that's all you intend to do with it, a .30/30 is arguably a bit lacking (but not lacking very much) so a .300 Savage, a .308 or a .30/06 hits the sweet spot.
Recoil management is a three legged stool. One leg is cartridge power, another is the weight of the rifle and it's fit to the shooter, and the third is shooting technique. The more powder you stuff behind a 180 gr bullet, the harder it will kick, and sometimes that additional recoil comes without benefit of an increase in velocity. These days the trend is towards lighter and lighter rifles, and a light rifle will kick harder than a heavier one. If your rifle must weigh more than 10 pounds so you can tolerate the recoil, are you going to enjoy dragging it through heavy cover? Most factory rifle stocks are cut too long for the average rifleman. If you have to shorten the stock to make the rifle fit you, you are also making that rifle a touch lighter. I won't touch too much on technique except to say that if you technique is poor, the recoil will seem worse than it needs to. If you shoot off-hand, and you have the butt placed firmly in your shoulder, you drop your elbow to close and protect the shoulder pocket, you shoot from a boxer's stance with your forward knee slightly bent, and your balance over your forward foot, the recoil will move across your chest, and down your rearward leg, making the recoil as manageable as it can be. As your position gets lower, even with good technique, recoil will seem harder than it does from off-hand.
So lets consider 3 rifles, a .308, a .30/06, and a .300 magnum. The .308 has a short action, it works well with a 20" barrel, so the rifle is shorter and lighter than the other contenders, while producing the terminal performance necessary to humanely kill large game. The .30/06 is usually encountered with a 22" barrel, some are 24", the action is long, and the weight will typically be a pound and a half heavier than the .308. The .300 magnum is usually equipped with a 24" barrel, but can be 26" and is typically a pound heavier than a .30/06.