I'd also say that Chrome in Kiosk mode should be suitable for the locked down account - just too lazy too take a screenshot of that, while Mr. porro already stated it.
Looks like your are describing kiosk functionality. There are distros developed exactly for kiosks, but as others said here - better to know variety of devices before hands.
You list ubuntu and chrome os, but appear not to have used any linux system modified per your preferences for long. Why chrome os/ubuntu? Looking for some feature present only in these ? If devices can be listed, choice narrows. If experiment with a few distros, options ( and questions ) will multiply and help build a stable system. Unless the exercise is academic (Q & A) and you are not seeking am image file.