It's a bit of a side trip, but since you say you have no experience with this type of programming, you might want to start by building an emulator for the Universal Virtual Machine from the 2006 ICFP programming contest. This is a task that takes an experienced programmer 90 minutes, but many teams with no experience were able to complete it in a few days. When you finish the emulator it unlocks a bunch of fun stuff, and it might be a good warmup before you tackle the Z80.
