As a teenager with all the activity you usually have pretty strong and flexible ankles. If you get him boots, get him some light ones though, I'm not sure he'd fine for his first time in heavy boots and carrying a backpack (or you could train for some day hikes, since you've got until November). You've got some reviews here :
http://www.outdoorgearlab.com/Hiking-Boots-Reviews but it's around 100 $ minimum. Keen and Moab usually have pretty good shoes/boots under 100 $ (at least in the US, you would have to find them on sale here). Their main problem is usually durability, but since you're saying he's still growing, it shouldn't be a problem.
I wouldn't start cold turkey with some Zamberlan/Scarpa heavy boots, that's the perfect recipe for an injury. Although heavy boots support the ankle, lifting them can be exhausting for your legs or Achille's tendons (I got that after a 7h day hike : needed a week to recover). Besides, it's usually during your teenage years that you realize if you need orthotics or not. I found out when I was around 12/13, one leg is longer than the other, which made my right foot hurt like crazy. Finding out on a long trek with heavy boots could be very unpleasant. Another reason for getting him used to walking long periods of time before tackling this.