My go to chambering for antelope to elk size game is the .300 WM loaded (with 180g and up, mostly Berger bullets) up to 1K yards. This is NOT going to be the last time you will be faced with this kind of decision, when you get the LRH bug.
As far as your recoil sensitivity, muzzle brake is your best option. I understand it is not for everybody but it is very effective for the money. Most of my rifles sports a muzzle brake or suppressor; it serves two purpose, reduce felt recoil and muzzle rise allowing you to spot target on impact - PRICELESS. There are many well designed and reasonably priced muzzle brakes out in the market from $50 and up. If you get a rifle that is already threaded to accept muzzle device, then you're set for a muzzle brake or suppressor. If not, threading the muzzle is ~$100.
Just to give you a general idea, the felt recoil on all my .300 WMs propelling 180g is similar to that of .243s. I am not recoil sensitive and shot the .300 WM for nearly 25 years without muzzle brake. Started using muzzle brakes in 2003 and never looked back.
Just a thought for your consideration.