My son is now 14 and started playing the drums at about 8 years old. His first kit was a 5 piece mapex kit, used from gumtree I think. Cost about £150, including some (not so good) cymbals. Make sure you get what is known as a fusion kit, as the toms will be smaller so easier to use when they are small. We put some new heads on it after a while, and it sounded pretty good.
I love hearing him play, and he sounded pretty good pretty soon! But it is loud. Luckily they have a short attention span when small so don’t play for too long. Make sure to get some decent ear plugs for them to protect their hearing.
Encourage them to take grade exams, my son loves the sense of achievement and the higher grades get UCAS points for uni. My son is now doing grade 7 ( goes up to 8).
I also sometimes have a go myself and love it! My son now has bigger drum kit, a rock kit, 7 piece with quite a few (expensive) cymbals.
Go on, get one! And no, please not an electric one, just not right. And if it comes with some of those silencing pads, bin them too ;0).
Simone