I have (2) 7mm and (5 or 6) 300 win mags. I haven't ever hunted with the 7mm's as i am a 300 win mag guy. I have killed many deer, elk, and moose with my model 70 Winchester and wouldn't use anything else. I bought my first model 70 (Chester) for my 16th birthday when i was in high school and i never thought it kicked much. I guess recoil has never bothered me so to speak. Only gun that i ever shot that i thought it had a push was a 416 Rigby ( i think if my memory serves me right).
I always bought guns from friends or from ads when they came up for sale. Could never have too many we used to say. That is until you get old and have to move. I guess my son will have that problem once i am gone.
Anyway get one that you like to shoot that doesn't make you flinch and holds a good pattern. They all work but the bigger game in the wild is much harder to bring down once their adreneline kicks in . Get a good bullet that patterns well, and practice on hitting the sweet spot, that is the most important thing. If you can't consistently hit your target at 300+ yards DON'T be shooting at that yardage! I hate it when people do this. We owe it to the game we are hunting to do it in a quick humanely way as possible. Don't make them suffer anymore than is needed.
Enjoy elk hunting, the work starts once the elk is down. I miss it a bunch and cherish the years that i could do it.