You might find this helpful.
http://www.go2gbo.com/forums/hr-cent...#msg1098406584
I would say everything above the 45 colt is a potential.
First number is lbs of recoil, second is foot pounds of energy on target.
357 Magnum 3.4 912
223 Remington 3.6 1272
22-250 Remington 5.5 1623
7.62x39mm 7.3 1496
44 Magnum 7.5 1298
357 Maximum 8.3 1723
30-30 Winchester 8.6 1577
243
Winchester 8.6 1978
45 Colt 8.7 1537
38-55 Winchester 10.4 1418
25-06 Remington 12.0 2228
7mm-08 Remington 14.5 2460
445 SuperMag 15.4 2236
270 Winchester 15.7 2588
280 Remington 15.8 2504
308
Winchester 16.7 2680
30-06 Springfield 20.6 2968
444 Marlin 25.1 2652
35 Whelen 26.8 3211
338-06 27.1 3471
45-70 Govt I 27.5 2317
500 S&W Magnum 33.4 3403
405
Winchester 33.4 3182
450 Marlin 37.6 3321
45-120 Sharps 37.6 2822
45-70 Govt II 40.8 3417
45-70 Govt III 44.6 3923
If it was me, I'd start him out with a Handi Rifle in .357. Start him shooting with 38 special rounds, as those are softer yet, and half the price.
When he is ready move him up to the .357 mag loads. Those should reach to 150 yards IMO.
When he is ready to move up I'd look long and hard at the .44 mag, or ream the .357 barrel to .357 max. Either should take virtually anything that gets close enough. So then it is up to the hunter to learn how to get close.
By the time he needs something that reaches more than 200 yards he'll have grown enough to be able to handle the recoil.
Like your son I didn't not get along with recoil, I did end up buying a .243, and over time I learned to be deadly on varmints with it.
Deer, well those experiences were not as good.
Start him out with Handi Rifle around 300$ and give him some years to grow.