Is he a big kid?  I would steer away from the youth sized rifle.  They are so small and light, that even a small caliber kicks pretty hard.  My son started shooting at about that age, and one kick to the shoulder can really dampen their desire.  I would go with a full sized gun with a heavy bull barrel.  The extra weight lessens the kick, and you will be toting it for him anyway.  My son shoots  my Sendero in 25-06.  With the extra weight, it kicks like a 22-250.  I have a friend that has the remington youth(model 7?) in 243.  The thing kicks like crazy because it is so light.  Savage makes a 308 with a heavy barrell(model 10fp I think).  That may be a good choice.

If you want to buy a rifle that is fitted to a smaller hunter, I don't think you can go wrong with a Model Seven Remington (Youth Model) in 243. If that's a little more than you want to spend, NEF makes single shots in a number of calibers that would work.

There is another alternative. Winchester, Remington (and possibly others) have started loading what they call "reduced (or managed) recoil" loads in a number of popular calibers. They use a lighter weight bullet with a reduced powder charge and have cut the recoil by half or less. They are very effective to 200 or so yards. You could find him a used gun in 270 or 30-06 and, if the stock is too long, cut it down with the possibility later on of restocking it as he grows.

The 22-250 is very deadly if you use the right bullets. I use the Federal Premium with the 55gr Trophy Bonded Bear Claw and have killed a number of deer with it. Federal also just started loading the 60gr Nosler Partition in 22-250. I haven't used any yet but they should also work great. The only negative on the 22-250 is that the less energy you have in a load, the less room you have for error. Of course, if the recoil prevents someone from shooting accurately it doesn't matter if you are shooting a 458 Win. Mag. if you have a poor hit.

Good Luck and Good Hunting

I have a Six yr old that shoots a rem m788 22-250. I handload 60 nosler partitioned that are great but I feel are a little light. I have a Rem m7 7mm-08 that I load with a 120gr Barnes X bullet and 37.5gr IMR 4895 that he shoots better than the 22-250 I try to keep him within 100yrds. The Model7 is an older wood stock and 18 1/2 in barrell minimum recoil and also a gun a youngster can grow with. Perform just like the big guns

My first centerfire rifle was a Harrington & Richardson (NEF) "Topper" single-shot breakopen with two barrels, .30-30 and 20-guage. H&R/NEF has many different calibres available in their handy-rifle, and they have heavy-barrel versions too. For my daughter's first real hunting rifle (and possibly for her mother, too), I'm considering a bolt-action in 7.62x39mm Russian. But since she's only 3 1/2, I've got a while to ponder about it. ~Rick