VPS is not that much, especially if you aren’t storing a ton of media. Digital Ocean and Hetzner are good places to look. This will also prevent some networking headaches you’re likely to have hosting it “on prem”.

If part of your reason for doing this is to involve the kids in the process, then it’s better to do it locally. Someone in the org has or can find an unused desktop computer that you guys can have fun with for pretty much zero cost. You will probably have trouble trying to connect to it from outside your network though.