I don't think I can get my hands on a floppy drive, but I still have an ancient computer somewhere with a DVD player in it. While not as cool, I had been considering turning into a simple media station for the specific purpose of letting my kid pick what music to play or video to watch by herself, without needing a screen to navigate it.

Like you, it never occurred to me that I can also just use specific DVDs or CDs as hooks for videos to be streamed, or media downloaded on a hard drive. So that suddenly makes the whole project a lot more interesting, and possibly easier too.

Buying a large pack of burnable DVDs is a lot cheaper and sustainable than using SD-cards like other commenters suggested.