Distro or software to allow restricted set of programs

I'm looking at setting up a machine as a video conferencing PC. I want to deploy it to end users as an indestructable PC, where if they start it up, it presents them with a menu that allows them to run exactly 3 programs (web browser, another video conferencing program, and pavucontrol to set sound settings). I was thinking of using XFCE or another lightweight window manager to do this, but was wondering if anyone knows of a kiosk PC style distro where you can lock everything down, and possibly allow immutable config, so the end user can change settings while the PC is on, but as soon as you restart, it goes back to a precoded set of configs. Sean