I’ll counter with the following: if you aren’t sure whether your kid will like it, it’s probably a better idea to start with renting. You’ll typically get a fully-serviced instrument with coverage for accidental damage.

Yes, it’s a fully sunk cost, but it’s predictable and you don’t have to deal with the hassle of selling off an instrument if they don’t get really into it. Once you’re confident that they’re going to stick with it and know they can handle and maintain it carefully, then you should look into buying.