I would give him the .308 to start with. It should be fine, recoil wise, and is a very adequate deer rifle. It is also notorious for it' s " built in" accuracy.
I started shooting a bolt action .30-06 when I was 14. I was about 125 pounds or so then. It was a Sears Model 53. The garand may be a little awkward for deer hunting though. So I' ll give another vote for the .308.
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Sorry about your loss as well visitor. Congrats on the grandchild making it to an age and being ready for the woods as well! I too will say let him use the .308. It is MUCH more practical and useful than a 30/30 and is' nt anything that really will need ever to be replaced for hunting in other areas or for larger game!
Sorry about your loss. I have a 13 year old son that killed his first deer at age 11 with a 243 and the past two seasons he' s been shooting my 30.06 and handles it very well. I handload 130grn bullets in it and that helps a little with the recoil. I' m in the process of buying him a 25.06 for Christmas. Out of the guns you mentioned i would also go with the 308.
On the other hand, I am glad his son is doing things that his father liked. I think the .308 is perfect for him, maybe he should start practicing with the .223 and get familiar with guns (if he hasn' t shot before) otherwise I will go with the .308 too!
I would have him start shooting the .223 and developing good habits and not flinching. Once he is comfortable with the .223 then have him shoot the .308. My nephew is 15 and he shot a savage .308 last night and you could see the recoil was a little much.
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] I am sorry for the loss. 
