One of my many side projects is a Z80 based system. One version was built as a shield style circuit on top of an Arduino Mega. I used the Mega for clocking, and to read/write the data and address bus, providing a simple serial interface. One of these days I need to revisit it.

It's about the easiest processor to get booted, technically. It has static ram for registers(so, no refreshes required), so you can wire the data bus to ground, the address bus to some LEDs and watch it step through the 64k address space with a manual switch for a clock if you want to.
If you want to get started with it, you might look at Steve Ciarcia's book on building a Z80 computer from scratch.
https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.pestingers.net/pdfs/other-computers/build-your-own-z80.pdf&ved=2ahUKEwjQzN-9ys_qAhXxN30KHSPFBVYQFjAMegQIBRAB&usg=AOvVaw1NYltLapAMZDnUWhyecUjz