Biglmbass,
This is just my .02 but I too started my son deer hunting a few years ago. Ibought him a youth .223 knowing that we would limit our shots to short ranges and only ideal shots. we shot all summer and before season started i found that he would rather shoot my 7x57 handi with his youth stock on it than his own .223. In his own words,"it hurt less and jumped less". I attributed this to the weight difference and since we hunt from a blind there was no need for a superlight carrying rifle so he shot the 7x57. He has in the last 4 seasons harvested 6 whitetails and 4 hogs with this set-up,at ranges between 80 and 165 yards, all one shot kills and none traveled more than 10 feet,most falling in their tracks.
Being that the 7mm-08 is a ballistic twin of the 7x57 and has yielded wonderful results for myself and countless others, if I were doing it all again today I would not hesitate to order the regular handi in 7mm-08 and also a seperate youth buttstock. When he outgrows the youth stock, I would simply switch back. With the weight of the gun working in your favor, recoil should be very manageable based on the recoil of my son's 7x57.
Good Luck hunting with your son and I am sure with the advice of all the knowledgeable guys on this forum you will make the perfect choice for a rifle. I know I have learned a bunch just listening in.