Be very careful of some of the advice you get on the internet from some well meaning folks who know "a little bit" about guns or hunting before you buy anything.
First, you talk about "one gun" for up to bear and elk. That means that you are likely to be undergunned for the elk, or have more than you need to kill coyotes or foxes near your chicken coop.
Second, a hunting rifle (and it's recoil) can be managed, as you don't take a larger hunting rifle out to shoot 50 rounds at the range. You shoot to zero the gun, and you shoot to stay sharp, but the recoil is enough to bother anyone, male or female. I know lots of big guys who have developed a flinch, and as a result, shoot poorly at game. If your first shot is a good one, it is enough. Muzzle breaks are great for reducing felt recoil, as is proper fit of the stock.
Thirdly, you can have a muzzle break installed on any rifle. They are louder, but so what. If it reduces recoil and helps you shoot better, that is what counts.
Fourth, the minimum caliber sufficient for the average person to kill and elk, is the .270, but many people still consider that too light. The .30-06, 7mm Mag, and .300 Winchester Magnum are what most folks use on elk and or bears when using rifles. There are lots of new calibers as well, short magnums, etc. and many are great. Most guys will tell you to buy what they bought. Keep that in mind.
Fifth, what kills large animals is a well placed shot, a well constructed bullet that expands without breaking apart even when it hits bone, and a rifle that can send that bullet with sufficient speed and accuracy. Many people are poor shots, and many use poor bullets that fragment before they get t o do the necessary damage to kill the animal.
I strongly suggest that you find a good gun dealer who will work with you to set up a nice rifle. You can get aftermarket youth stocks, or alter an existing stock, but the caliber, recoil and weight are the first things to consider. After that, a good scope and a well adjusted trigger. Go to a few gunshops until you find someone who really wants to help you as opposed to just sell you a gun.
Have fun and be safe.
Pete