You can get a usable smartphone for well under 100 USD on AliExpress or a reasonable secondhand one from a reputable brand for about the same price here in Norway on online trading sites. Don't teenagers get pocket money or do weekend jobs any more? My sons were grown up by the time smartphones were affordable but No. 2 son bought his own Siemens C65 with saved up pocket money when he was in his early teens.

You only need $25-30. It'll be locked to a carrier, but that doesn't matter and is perhaps preferable (no monthly fee for a subsidized device) if you are able to use wifi. There's an ETA prime video which explores using a 2025 Moto 5G as handheld game console: https://www.youtube.com/watch?v=5ad5BrcfHkY

tl;dw it's quite capable for the money and would could easily get on social media apps/sites.

You can get smartphones for 80 dollars (like the moto E15)