If you are worried about the loudness of an acustic set , you can always put silensers on the drum heads and even cymbals. I'll even say that they are
required if the drum is played in small spaces; a big basement is way too small for a drum kit. There're plenty of manufacturers that sell silensers. I used to put old shirts on my drums, the stick bounce is pretty bad but it'll do.
I would steer away from an electric drum set as a starter drum kit. They have completely different 'feel', in fact they are different instruments, kinda like an electric bass and a upright bass, two very different animals. If you get the electric kit it's likely she/he would eventually gravitate towards keyboards than to continue playing drums.
Either way, it's good that there're kids that are still interested in playing music and parents that support them
