For what it's worth, I grew up in similar country, northern NY, and learned hunting in Lewis and St Lawrence counties in the western Adirondacks. That's left me with some strong opinions that may fit your question:
I like hearing that your son is using a peep sight. Get a rifle that works well with iron sights and put a peep/receiver sight on it. Let him learn big game hunting and centerfire rifle handling for awhile before going to a scope. He will have better skills in the long run.
Generations of northeast hunters started with the 30/30. It's still just about perfect for deer and black bear within 100 yds. My first rifle was a Savage 99 in 30/30 (its not my only rifle, but I still have it, still has a peep sight, its 93 years old and going strong - not me I'm only in my 50s!). My brother still has his first deer rifle too, a 30/30 94 Winchester with a Williams receiver sight. My father (who is in his 90s!) started with a 38-40 Colt Lightning Rifle - I don't recommend that!
If you don't want/like/find a 30/30 there are lots of solid options. I'd recommend staying with short action cartridges. I just can't see starting a 6 yr old out on a long action rifle, and there are lots of very versatile short action cartridges out there. Please be careful about going too small in caliber. Yes, 223s, 243s and the like will kill deer, but a young hunter is not always going to make perfect shots. Larger calibers can be a little more forgiving and leave better blood trails. I'd probably not go below a .250 Savage or .257 Roberts, anything 260 or larger based in the .308 are good choices. The 7x57, 300 Savage, 32 Winchester Special, and 35 Remington are great classics. I don't know much about the 6.8 SPC but that might be an option.
I wouldn't start a new hunter with a semi-auto, but if you're a fan and he handles them Ok that's your business, but it will limit your cartridge options.
This is getting long. I'll quit for now.
