The first two things I'm planning to do are:
1. implement a Z80 test circuit that will let me just blink some LED's or whatever they do. This is apparently one of the most basic things you can do with a Z80 and doesn't require much in the way of supporting components and what-not.
2. Figure out how to write bytes to, and read bytes from, an EEPROM using an Arduino. I found a bunch of Youtube videos and websites on this topic, to use as resources.
Sometime after that, I'll start investigating what it takes to read a program off the EEPROM and execute it.