I would suggest the .270 as it's the perfect deer rifle but the .243 will do the job.
See the recoil numbers on this chart... .243 is 8lbs., .270 is 16lbs., .300 Win Mag is 23lbs. etc.
Rifles will make a difference also. A Ruger .270 gives you a little bump but the .270 out of my Remington 700 gives me no problem. Difference in stock designs I guess.
.243 is probably what would suit you.