Find the cheapest MP3 player possible, maybe one of those built like a USB stick that can plug into a computer.
Here’s one. There might be better options out there. The idea here is no wifi, no Bluetooth, etc. You could presumably load MP3s onto it just like you could a flash drive. Unlike the flash drive, it can play it back.
As far as ripping CDs, I use EAC. It supports ripping compressed to MP3, among other things. The linked player can play FLAC as well. I imagine most can, but the larger files size of FLAC might become an issue. Other programs exist, of course. It can be done!
Double post, but focusing more on the real computer. Do you have access to a library? Sometimes they have computers people can use. You might be able to load a program to rip onto a USB stick and run it portably (that is, without installing it onto the computer.) Not ideal, but if it’s Windows I think Windows Media Player can rip CDs natively.
In that case, bring in the CDs and the MP3 player, rip the CDs, then load them all at the library. There might even be CDs at the library you can check out as well.