4ths, 5ths, whatever the count is up to on the 7mm-08. a .243 is also a good round, its very flat and accurate. it will do just fine on open shots on deer sized game out to 300 yards or so. farther with the right bullet and shooter. i would give the edge to the 7-08 though, for a little bigger bullet. the .243 does real well, and i know a man thats killed an elk with one (neck shot), but if you have a quarting shot or try to bust through a shoulder, it can be a little light. again, will depend largely on the type of bullet used.
i have an '06 as well, and i put a sims vibration recoil pad on it, and it significantly reduced the felt recoil. i went from no pad at all to the sims and noticed a huge difference. you could try that route, and also look into one of the shooting pads that you can put on over your clothing. that may be enough to allow you to shoot comfortably and keep your favorite rifle. the '06 is a fantastic all around cartridge, i know you'd hate to have to let it go.
you can also look into getting a heavier stock for your rifle, the added weight will reduce the recoil some by absorbing more of it in the bulk of the rifle. the tradeoff is having to carry a heavier rifle. a muzzle break will decrease the recoil, and maybe significantly. but your going to add a lot of noise. you will want to always use hearing protection with one (i know most folks don't while hunting, myself included usually).
if you decide to get a new rifle, you should also consider the weight of whatever one you get. the individual rifle will kick differently in the same calibers with different weights, stocks, etc... so swapping stocks on your current rifle might just solve your problem. its not always the caliber. my .30-06 is now a kitten, a buddy of mine has a win mod. 70 that kicks like a dang mule, both bolt actions, but different weights and different recoil pads and stocks. everyone's sensitivity to recoil is different, and with a shoulder injury i can't say for sure what you can or can't tolerate.
a cheaper rifle you may look into that has almost no recoil is an hr handi rifle in .243, with a heavy bull barrel. my good friends dad has a horrible back, and cannot take any recoil whatsoever, and uses this rifle. he says with the heavy barrel it has no kick whatsoever. good luck in whatever you decide.
