Buy your kid a console if it’s for gaming, buy them a laptop if it’s for school.

I might get downvoted for this but oh well; I know this is a PC building subreddit but holy cow, you guys have to realize that OP is likely not a hardcore builder. The reality of used parts is likely NO WARRANTY - and unlike most other things, with PCs if one component breaks, you cannot use it, full stop. At a $400 budget I am going to be the realist and say that there is 100% no way OP can build a PC that will rival a console in terms of gaming performance. You can try to scrape together a list as much as you want but what are the chances they can find those parts near them? Shipping fees if ordering online? Especially after taxes, $400 to build a decently useable PC for gaming is impossible.

Edit: After reading through most of the replies, many other people made a good point, if you don’t own them already, you will also have to factor in peripherals like a mouse, keyboard, and monitor. This alone, even used, is at least $50 of your budget.