Sounds like you're gonna have some huge fun time :) Same here, software developer turned hardware tinkerer.
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.
2. I bought an 80s EPROM writer from a forum for E1 which I use for that; because it's so old (and slow), you can actually understand and measure what everything does.
And here's the good part: These days, a basic scope is incredibly cheap!
Check ebay and/or amazon for a DSO138. It's a simple creature but ideal for a project such as a Z80. There are two variants of the DSO138 - kit form and pre-assembled. Prices are an astounding $25/$30 respectively.
Unless you just want to spend 4 hours soldering (not a bad thing), spend the extra $5 and get the prebuilt. And make sure it has the latest firmware (cleaned up some bugs, improved centering, and reduced noise).
And @mindcrime - please blog that project! I know I speak for loads of others when I say I'd love to watch your progress. I never get tired of seeing others do cool stuff I don't have time for anymore. :)