Got a young guy that needs a reasonable used laptop, in the $2-300 range. Looking for smooth but not spectacular graphics, and a 15" screen or better. Preferably with 2 drive slots so he can have an NVME or other SSD for the OS and a large rust drive for installing games. It's going to be plugged in when used, and weight isn't a great concern, it's just for travelling with.
IMO your best bet at that price range would be laptops with an AMD APU as the integrated GPU is really good for moderate gaming. If you live in the US, there's for example this auction on Ebay (currently at $241.50): https://www.ebay.com/itm/355230104508 . For that particular laptop, I don't know about the drive slots but apparently it at least has one slot of upgradeable RAM so that's a big positive I guess: https://www.crucial.com/compatible-upgrade-for/asus/vivobook-16x-m1603
You can start from there and look for similar specs on Ebay. When in doubt, just copy the name of the integrated GPU and search "[whatever your son is playing] + [the name of the GPU]" on YouTube, or just look for generic benchmarks.
Thanks for the suggestion on AMD re: APU graphics. I have a 2500U laptop thats a bit underpowered for what he's needing, but that one you linked might fit the bill, if the bids stay sane. Ill keep an eye on those sorts of laptops.