Nathan,
Based on my experiences growing up, as well as bringing up my daughter, and now bringing my grandson into hunting and shooting starting when he was 5 I can recemmend the following.
I started just before I turned 6 with a M1 carbine as it was all I could fully support at the time the following year I moved up to a 243 Win. which I still have. My daughter started out using the same Carbine for target as did the grandson. The daughter quickly moved into the .243 and was deadly on paper to 200 yds from hunting positions then argued with me when it came time to shoot her first deer at age nine and proceeded to drop it using my 25-06 at 180 yds. using a erst of course. She is now 25 and the owner of that rifle.
The grandson wanted more than anything to shoot a hog a couple of years ago. WEll he is one of those stubborn red headed kids who just don't take no for an answer. So I brought out the M1 for him as well. I also got out all 3 .243's and he wasn't big enough to hold any of them at the time. He was just about to turn 5. He managed the M1 very well but I knew it wasn't exactly the best thing I had for a hog of any size. I also had a Ruger compact in .308 that he kept insisting he wanted to use. I used it for about 90% of our hunting and he knew it would put one down. I knew if he pulled the trigger on a full load round I would probably be explaining the bruised shoulder to someone with a badge. Anyway I settled on the reduced loads posted on the Hodgdon website under Youth Loads. WE used the 125gr load to take his first hog with one shot just before his 5th birthday. Since he has gotten a few more with it and we have bumped the load up as he could tolerate it. We are now shooting the 130gr Barnes TSX at 2500fps which is a very deadly round out to 200yds. The boy can shoot them from the stand or from the hunting rest into around 2" groups at that range. He is 6 now and hsa all the confidence you cold ask for in the rifle and load.
When I was looking into getting him his own rifle as your doing I looked at them all. I almost decided to go with the Weatherby Youth Vanguard as it come with two stocks.
http://www.weatherby.com/products/guns.asp?prd=Rifles&prd_sub_type=3&prod_code=VGC223RR0O
The calibers from .243 up through the .308 are all deadly with practice and limiting shots to certian ranges. I am fortunate enough that we own our own property and we set up our tree stand and practice from it as well as from the pop up's. I set out several full sized deer targets at various ranges and let the boy shoot them. After 5 rounds to each as I call out which one to shoot we move them to different places and shoot some more. Different angles behing treees or anything I can come p wth at the time to make it as real as possible. He is a very accomplished shot for a 6yr old as is the daughter, who will shame most seasoned hunters with her shooting. IF you look at the bottom link under my signature there is a clip of the kid shooting that first hog, a few of his targets, as well as the daughter and a few of her accomplished shots. The daughters deer were all taken at over 250yds using the same 25-06 she started out with. THe hogs as well as the coyotes were all taken around midnight, between 100 and 200 using the flash light while out checking a hog trap.
Good luck to you and if your anywhere around Carters stop by and give the Rugers and the Vanguard a look. For a older boy I might have went with the Vanguard but due to his age and size I went with what I had, and am now out another rifle. LOL
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