Of all the suggestions, That right there is the one, 
(If you haven’t already bought one)
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the gaming is the big driver, any old PC will do everything else with ease. You might leave that part off the school PC and get him a console for that.
I’m opposite.. Im intel over AMD now.. Intel’s I Series chipsets are generations above the others now a days.. very impressive.. hell my first gen i3 laptop is still running fine with windows 10 and is about to get upgraded to win 11 here soon, it runs a 256 SSd and I forget how much Ram now, but it moves pretty good fo all i do.. of course i dont game on it. mostly I remote into it from my work laptop and do bills on it and use it as a storage box/server kinda unit. and i’ve ahd that box up and running since 2008ish..
only thing i did since then was really add some ram and upgrade to a larger ssd. cause it didnt have a ssd to begin with.. and that move alone like tripled speed.
We have had great luck buying refurbed laptops off Amazon. 3 Dells and all of them have been great. Get a CORE processor.
definitely get the best ryzen you can, the 7 (5825u) is better than the 5 for just slightly more..
it’s that ryzen is apu, instead of just a cpu or gpu (like nvidia) . if you can’t afford a dedicated gpu along side your cpu (common with most laptops) you definitely want the ryzen.. although even when building with a gpu i would still opt for the ryzen tbh..