For the most part, you have been given some good advice here!
I agree with Vapodog too, the .308 can be quite a kicker. A lot depends upon the style of stock you have and the weight of the gun is a big factor too.
I have a light weight .308 and it has about the same felt recoil that my 7MM magnum has. I have had " scope eye" and five stitches from my .308 to prove it!
Now to repeat what some have said, there are many fine recoil reducing products around today. Try them out until you find one that works!
If all else fails, there are several good deer calibers that have less recoil than the .308. You may want to try one of them out!
Lastly, don' t get caught up in " what the others" are shooting! If all else fails and you end up going to a lighter caliber, there is nothing wrong with that!
I would rather see someone shooting a lighter caliber well, than see them flinching, wounding game and not having any fun!
While I don' t think that a person can be " overgunned," I also think that we shooters have gotten too caught up in " magnumitis!" Good luck!