Mint_Raccoon

I have a T480 that I’m very happy with. With shipping I paid a little under $250. It came with 16GB of RAM and a 256GB SSD (which I replaced with a larger one).

Some old Archos media players, such as the 605 WiFi, run a locked down Linux according to Wikipedia.

I know you said no Pokémon, but what about Digimon? I think something in the Vital Bracelet family might fit your needs. It’s a watch with a character that transforms into more powerful forms based on your activity. There is a bit of an investment since you’ll need to buy the device itself and additional cards for more characters. Another thing to note is that all models except for the Vital Hero are (technically) in Japanese (there’s actually very little text because the menus are mostly icon-based). It also has a companion app called Vital Bracelet Arena, which can serve a storage for characters and allows for battling characters with other people (there no way for players to communicate with each other, so you don’t have to worry about your kid talking to strangers). If this sounds interesting, then I highly recommend checking out Humulos for more information.

Debian is always a safe choice for almost everything. It’s also worth checking DistroWatch. They have a search that can filter which distros are developed for a specific task (it’s under “distribution category”).