Some good options on the table. Here's another one... Vanguard youth.
Vanguard® Series 2 Synthetic Youth | Weatherby.com
At 10 My son killed his first deer with a 14" TC Contender 7-30waters with a break(red dot sight). By 11 he could handle my 45LC, 7STW with break, and .257wby. I was not going to chop the stocks on the 7 or .257, and the colt wheel gun only gave him a 25-30 yd range. We ended up purchasing the Weatherby Youth .243. Great gun that grows with them with the stock extenders. He can easily shoot under 1/2" at 100yards with handloads. As far as enough power, he took a nice 2 1/2 year old buck at 434 yards with a Berger 95g. Next morning took a 5 1/2 year old 245lb 4x4 whitetail at 170yds. I would get him the same rifle again if I was doing it over again. So far in 2 years he has taken 5 deer (ranges from 95-434yards) with the little rifle. Not one deer has went more than 25 yards. The recoil is light enough that he regularly will shoot 50 rounds on one range day and still have enough in him to practice with his bow for a hour befor heading home. We did make it easier for him with a Leupold VX3 4.5-14 CDS and a rangefinder to make adjustments.