My strategy has been to get into 80s game consoles where assembly programming was expected but the platform is small and standard enough that I can use emulators with memory views/debuggers & see everything going on.
heck at the end I might even have a game!
I'm starting out on z80 since I have an MSX and I hope to move to Sega Megadrive/Genesis later since I hear nothing but good things about the motorola 68k. The z80 seems pretty easy to understand (though it's not always consistent).
It's worth checking the limitations of the video and sound hardware to see what you like as well. I'm partial to FM synthesis so Sega consoles make sense to me. 8-bit stuff is going to land you with really tough colour restrictions (often about 3 per 8x8 square, tops). You may want to start with the "16-bit" era, which generally used 4-bit colours (16 for the whole screen, easier to create assets for).