As someone who's been on 2 treks and spent 4 summers on staff at Philmont, i can give you some insight.
First, I wouldn't skimp on your boots. They will be your most important item on the trail. I've seen many people come off the trail due to either poor quality boots or improper fitting of their boots. The terrain is varied from flat meadows, to stream crossings, to climbing above timberline. The elevation range is from 6600ft at base camp to 12,441ft at the highest point. On my treks, I used a $200+ pair of Asolo goretex backpacking boots. They were heavy, but they've held up for 12+ years.
I would recommend something similar to this.
http://www.cabelas.com/product/Foot...rd1546137&WTz_l=SBC;BRprd1546137;cat104104980 It's waterproof and full leather. Nubuck or split grain leather will be eaten alive by the rocks, scree and weight of your pack.
You should choose a pack that will allow you to carry all your gear for the 10 days and food for about 3 days. (you'll be scheduled to resupply every 2-4 days). As a leader, you should pick a bigger size pack. You will most likely be carrying around 70-80lbs pack. The kids you're with will get tired and to keep them moving, you'll probably take some of their weight by about day 4 or 5. In addition, you'll probably need space for water reserves. Some camps you'll stay overnight at might be dry. This means the crew will need to carry all the water for drinking, cooking and cleaning for about 24 hours.
Be mindful of the weight of everything you bring. Do you have a sleeping bag/pad/tent picked out for you and your son yet? Do you know how the crew will be cooking? Philmont provides pots and utensils, but you'll need to bring your own stove. Are you thinking of white gas or butane canister stove?
Philmont was one of the greatest experiences of my life. We did close to 100 miles in 10 days. What makes philmont great is not just the backpacking, but the programs you will experience. The living history program is phenomenal, the staff is all great, and if you're prepared, you'll have a great time.
Let me know if you have any additional questions and I can let you know what to expect.