Simplest device for mini operating system
Parts selection is actually quite a lot of work. Especially to vague requirements. Even just the question of an LCD screen is complicated (what size? pixel addressable? integrated controller? e.g. Efficient display of simple text/graphics on color LCD by ARM )

Then there's the question of what architecture(s) your operating system should run on, what features it should have, etc.

The video appears to refer to some sort of generic PC operating system, designed to boot on the "bare metal" of a PC. For that you will be best off with an old or cheap laptop to start with.

If you want to build your own OS, ARM is probably a good platform to start with; you might be able to find a dev board with a built in LCD, that would save you a lot of hardware work.