My advice is always this: Hunt with the gun you are most comfortable with!
People always say you need a big gun, say a .300,.338, 375. What horse crap!!! While having all that energy can be a good thing, most people I know can't handle the recoil; and it causes them to flinch horribly. This causes a lot of animals to be wounded and suffer the rest of their days.
Personally I would rather take someone elk hunting that has a smaller caliber gun that can put all their shots where they need to, than to have someone that has a big caliber that can't get a decent group.. I know, I know, smaller calibers don't have a lot of energy compared to the big boys. But all that energy isn't worth a hill of beans if you can't hit the target.
Take my mother for example. She shoots a .308. And she has had no problems dropping elk out to 400 yards. Sure the .308 doesn't have the highest energy level but she can put 5 rounds in a group the size of a dime. It's all about shot placement. Another group of buddies hunt everything with a .243 win. and they have harvested all the big game animals the lower 48 has to offer. Sure they have to get a little bit closer, but that's the fun part. Trying to get as close as you can without the animal knowing you are there.
According to the CPW hunting brochure all you need is rifle cartridge of at least .24 caliber with a bullet weight of at least 85 grs. producing 1000 ft lbs of energy for hunting elk and moose.
So if you have a hard time with recoil don’t fret, just grab your favorite light recoiling hunting rifle and head to the range. Then challenge yourself to see how small of a group you can get. When you can get a small group don’t be afraid to head out to get that elk. Just remember to keep your shots within a reasonable range, and you’ll have no problem filling that freezer.