Most machines of that era had a pretty standard architecture except for a few strange ones like Atari and TI-99/4A (minuscule amount of ordinary RAM but a fair amount of “video RAM” the CPU can access through ports; no bitmaps, only tiles) and the early Sinclair (which used Lancaster’s “cheap video”
https://www.tinaja.com/ebooks/cvcb1.pdf to delete the display controller)
One thing that did matter was color choice. My TRS-80 Color Computer had a terrible choice of colors that you’d expect from a physicist or electrical engineer, the C-64 had a small number of hand-picked colors that looked nice. (Somebody ought to tell the people who maintain contemporary terminals because I usually have to do “:syntax off” to see what I am editing with vi and it was annoying as hell to set up a Linux computer attached to a TV this weekend because I was sitting at an odd angle which made most colors illegible except for white.)
Another interesting fact to me is that 1980s era display controllers were conceptually simple but had a huge part count in terms of gates because of multiple wide data paths. Today it is fun to build them with FPGAs but difficult to build them out of discrete parts. I saw an ad in Byte circa 1979 for a gfx card for S-100 computers that had much better specs than the average home computer but was a fairly large board packed with chips on both sides.
Thus most of the home computers had an ASIC display controller and projects like
https://www.commanderx16.com/
struggle and wind up using an FPGA or microcontroller for the display controller as opposed to something authentic. Sometimes though I think it might be fun to try building a display controller on a few big breadboards.