Keep the cartridge less than a .30 cal. The dilemma that "I would have" is deciding if a .243 is enough *** for the hunting you are doing. Whitetail deer from a ground blind, sure. For the top notch marksman that can really display a shinny example of shot placement at anytime....sure. If at least one of those two things aren't checked off and you are hunting some high country Colorado muleys or something, I'd maybe consider something a little bigger than a .243 but less than a .30 cal.
Next, as far as non cartridge related recoil is concerned, a heavier rifle, combined with a muzzle break will certainly help eat at some of the felt recoil, so those are some other ideas to consider as well. Downside is hiking in with a 14 lb rifle sucks. Two of my remingtons I use are 16 and 17 lb. and it's a strain to hump around on multi day hunts.
You can think out side the box as well. Spending money would be a risk, but a good tripod and a hog saddle could help lower some recoil as well if you know how to leverage the tripod...key being consistently.
Just some ideas.