Just to put some real numbers up to consider I used this site to calculate recoil of some chamberings you are considering. I picked a load suitable for deer hunting. You could get slightly different numbers using lighter or heavier bullets and faster or slower velocities. At least this puts it into a perspective that is easy to see and not subjective
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http://www.handloads.com/calc/recoil.asp
I included a 30-06 just for perspective since since the 30-06 is considered about the upper limit that almost anyone can learn to tolerate. I can sympathise with your shoulder inury however. My 23 year old son is 6'2" and 250 lbs. But because of 2 shoulder surgeries earned while playing HS football he does not tolerate recoil nearly as well as I do.
If all rifles weigh 8 lbs you get the following recoil, with the loads I calculated
223, 60 Gr bullet @ 3150 fps----3.5 ft lbs recoil
243, 100 gr bullet @ 3000 fps---9.5 ft lbs recoil
260, 120 gr bullet @2895 fps----11.3 ft lbs recoil
7-08, 139 gr bullet @ 2900 fps---14.4ft lbs recoil
308, 150 gr bullet @ 2850 fps----15 lbs recoil
30-06, 150 gr bullet @ 3000 fps--19 ft lbs recoil
If you were using a lighter rifle recoil would be a bit more, a heavier rifle and it would be a bit less.