Z80 is an artifact of the past ..
If I were you I would just forget about this name ..
However, if you would like to be very close to this project, you can consider 8051-derivative, for example, the AT89S51 ..
This 51-core microcontroller has the same background as Z80 (developed from 80XX-family) but it has oscillator, RAM and program memory build-in ..
Also, translating existing code wouldn't be difficult:
Instead of LD A, 3Fh you will use MOV A, 3Fh,
Instead of JP Start you will use LJMP Start .. and so on ..
The equation looks like this:
89S51 <=> Z80 + 7414 + 7474 + 2716 + 6116 + 74138+ 7432 + Z80PI0 ..
To make you even more confused, I would construct this project with PICAXE microcontroller, for example the PICAXE-18X ..
PICAXE microcontrollers are basically PIC-based units with BASIC interpreter, so practically someone who is not familiar with microcontrollers can learn how to pogram them in almost no time, and on top of that they can be programmed (burned) using any PC with serial port without external hardware ..
If you need more info on PICAXE go GOOGLE ..
Regards,
IanP