IMHO you can't really go wrong with the 243. It is a flat and smooth shooting gun. It won't be heavy to carry into the woods and it will get the job done up to a good distance. My younger cousin uses a 243 with a bull barrel and it is one of the best shooting guns I have handled.
I am partial to my 7mag. I don't think it has much kick to it but then again I don't have back problems.
You can put weight in the stock of any gun you get to help reduce the recoil. You can also put a better pad on the stock (I've heard a lot of good things about the Limbsaver recoil pad).