You don't really need a full blown retro computer for all that. There are plenty of "modern" (as in "in production and in use") 8 bit embedded CPUs out there.

Arduino/atmega comes to my mind, just ditch the IDE. Instead program assembly and assemble + program the board using their toolchain. Of course, at first the analog part (CRT, old keyboard) will be missing, but these are not needed to write your own little kernel. However, I did a quick search, and it seems the Arduino can interface with a VGA display: On the hardware side of things this only needs some resistors, and software side could be deemed as an interesting exercise ;-)