Bear, I just had my first custom rifle built in a 6.5-06. It sports a 29 inch barrel, 8.5x25x50 Luey LRT scope, weighing in at 13 lbs. The stock was measured to size for my short reach and I had a muzzlebrake designed by the 'smith. I swear when I am shooting it, it feels like an air gun firing pellets.
I'm a little guy and the first shot I ever took with a scoped rifle placed a half moon directly over my eye which I still wear proudly. As a result, I have always been a bit recoil shy. I have gotten over it to a degree but it still lurks in my mind when shooting my hunting rifles at the range that do not wear a brake.
I believe having a stock fitted properly, a muzzlebrake installed, a high quality recoil pad installed, proper shooting technique (which i am sill working on), and proper bench equipment, you should have no problem with any of the calibers mentioned above. I know muzzlebrakes aren't the most popular to people sitting next to you, but if you have never shot a rifle with one, I think you would be amazed at the reduction in recoil that they alone will provide. Good luck with your surgery, i hope it helps! Jim R
Bear, if LR target shooting is what you are after, I would recommend the many 6mm cases starting with the 6BR going to the improved wildcats using the 22/250 case. Improved 243's are very hard on the throat. The wildcats you are looking at are also very tough on throats.
105 to 115gr bullets at 3000fps will get you to 1000yds and beyond. Recoil is very comfortable in a portable rifle. If you put a brake on it, you could build one under 8lbs and it will feel like a 22LR.
If you also want to do some hunting, then I would strongly recommend a muzzle brake with whatever you choose. I would look at the 6.5mm as the smallest calibre for LR hunting and work up from there.
I know a guy that has a very expensive custom titanium rifle in 300win mag. With its muzzle brake, it is a light recoiling rifle and at under 6lbs loaded, a joy to carry. Not sure who made it but it shoots well.