I started my boys off with H&R .243s and they became proficient very quickly, but both took their 1st deer with a 7400 30-06 (Oldest was 11, youngest was 9), and both have stayed with the .308, 30-06, or .7mm mag (my father in laws, their uncles or my rifles) until I bought them their own 30-06s. (Neither have ever seemed to be bothered by recoil).
Had I to do it again I would have started both with Marlin 336s in 30-30. I have shot both them and the H&R .243 and to be honest 150gr winchester 30-30s seem to have less recoil than the 110s from the .243. Of course neither are bad, and as most new hunters should not be shooting at 300+ yards the 30-30 is really plenty of gun anyway.