Another vote for electronic drums and headphones.
My BIL's little brother was ALWAYS making noise when he was a kid, and drumming on things. It drove the family and his teachers crazy. He begged for drums, so his parents started him out with the electronic drumpad. What a great investment! He learned very quickly, stuck with it, and is now a music teacher at their family-owned preschools.
He did eventually graduate to a full regular drum set, as well as the guitar, and some brass instruments, but by that time his skills had developed enough that it was really a treat for his parents to hear it.
My dad is a drummer too--wish I would have picked up his sense of rhythm! My dad plays in the basement (not soundproofed) and it IS very loud. Depending upon how your basement is finished (or not) you can get acoustic foam to put on the ceiling or between the floor joists.
If you have a larger budget (way down the road--if he sticks with it) you could even build a soundbooth. I have quite a few musician friends who have recording booths in their basements.
ETA: If you do get headphones, try to find the ones that limit how loud the kids can turn it up. My dad has significant hearing loss from his lifelong drumming hobby.