Once they get going in the hunter/jumpers, they wear breeches and half chaps or boots just like the girls. Paddock boots to show when they’re on small and medium ponies.
But for camp, maybe ask them but if he’s more comfortable in jeans that’s probably fine! The main thing is boots that fit and have an adequate heel. The heel is a safety thing to keep feet from going through the stirrups.
For helmets, having an ASTM approved helmet that fits well is the most important thing but you can also use this VT rating system to inform you.
https://www.helmet.beam.vt.edu/equestrian-helmet-ratings.html