If you think the guy is going to be sensitive to recoil, then keep in mind that the 7mm-08 will have almost as much recoil as the .270 and the .308 will have almost as much recoil as the .30-06.
The .243 works quite well on whitetails. Don't let anyone tell you otherwise, because, if they do, they don't know what they're talking about. I switched from .30-06 to .243, and I've found that the deer don't go a step further after being hit with the .243 than they did after being hit by the .30-06. Here's proof that the .243 works.....