If you're thinking "old school" then your choices are NES, Gameboy, and 8080. Personally I wrote an 8086 emulator, to play space-invaders.
8080 is a reasonably simple system, without horribly complicated graphics or MMU addons. Interrupts were hard to debug, but otherwise it's a very well documented system with lots of directions you can go in afterwards - emulate DOS, and Hercules? Emulate CP/M? Emulate other games? Or start looking into running Windows even!
My one advice would be not to skip any parts in the implementation ("I just skip the cpu timing so I can have something on the screen quickly"), as many things are interconnected and changing things becomes very difficult later on.
All in all it's a really fun project and at least I learned a ton. My original motivation was to learn Rust, but it turns out that was the easiest part.