If recoil is an issue for you you might consider picking up a recoil shield such as http://www.midwayusa.com/product/284...d-ambidextrous
I have one that I use when I shoot my Mosin Nagant off the bench, that steel butt plate is a killer. The recoil shield would be great for practice with any caliber you chose allowing you to practice more. When it comes time to actually shoot the rifle at a game animal, I promise you that you won't even feel the recoil. Of all the deer I've shot I can't say I felt the recoil even once and barely remember even hearing the shots.
Now to answer the original question, I'd lean towards the 7mm-08, however the .243 would be a good choice also since you are recoil sensitive.