Bike for jumps in forest?

I ride road bikes, commuting and longer road rides, so I am somewhat familiar with bikes, maintenance and repairs.

My son, growing 16 year old, current 5'9", has recently gotten into riding to wooded parks with his cousin and jumping little jumps. He has been using his little sisters specialized mtn bike, that is too small for him, with a suntour shock she got used. I am not sure how old, but it has rim brakes and qr skewers.

He has saved some money. I am willing to chip in with Xmas coming. I unfortunately don't even know where to start with bike style or what is decent in that areana. Budget is probably £400-£500. Happy to go used.

What style of bikes should we be looking for? What brands and such? Also what are the red flags when looking at these bikes?