My parents bought me some tools when I bought my own car 1 year after high school. Until then I just borrowed Dad's tools, per his instruction. About the only tool I ever bought prior to that was when I lost something of his. Good thing he didn't care about matching sets.
That tool set wasn't much, a 40pc Great Neck socket and ratchet set, some Craftsman screwdrivers and some off brand pliers. It was to help me start fixing my car. Truthfully, they were fine for what they were, though the ratchet was a POS. Unfortunately, I got them stolen off the roof of my car when I went into work to make a phone call, because ironically I couldn't fix the car and it wouldn't start. I thought I was safe because I was parked out in front of the store and you could clearly see the car from inside. I was wrong, as soon as I walked to the store they were gone.
If it were me (I don't have kids), I'd buy some decent stuff, but nothing too expensive, and nothing you're too attached to either. It's likely to get lost or stolen, or.... Craftsman screwdrivers, Husky pliers, Kobalt sockets and ratchets, and that sort of thing. I had tools to be handy, not necessarily mechanical. Sure I could do some minor things with the car, but I could change out a wig wag on my used washing machine in my first apartment because of some basic tools.
I guess what I am saying is get him/her enough to get going and do simple things, either at home, or on the car. Let him/her decide what direction it goes.
*I now have so many tools I have a lateral file cabinet full, a chest of drawers full, about every 18v DeWalt tool they made and a 26" stack and a 44" HF full to the brim. They'll find there own path. My brother barely owns screwdrivers and sees no use for tools.