MacOS from scratch (post 2/2)
Select File -> Quit to exit Drive Setup, and close the "Formatting Software" and "Disk Utilities" windows.
Double-click the "Mac OS" folder and then the folder for the System version you wish to install. I chose System 7.1.1 here as a good choice - it's reasonably up-to-date, but doesn't use a ton of RAM like 7.5, and runs all the way back to the Macintosh Plus. (If you are unsure what versions will work on a particular model, double-click the "System Software by CPU" folder and then navigate to the model you'd like to run).
Double-click the "Net Install.scr" file to launch Disk Copy and mount all of the installation disk images.
Click "Agree". After a few moments the installer will launch. This will look different depending on the version you pick, my screenshots here are for System 7.1.1.
Click Ok to get to the main installer screen (for some versions you may go directly here):
The defaults are usually OK. Make sure it's "Macintosh Family system software" or "System Software for all Macs" or something like that (the phrasing differs per System version) to ensure the resulting hard disk can boot on any supported Mac.
Once the installer is done, you should see this success:
Choose "Quit", and then choose "Shut Down" from the "Special" menu to cleanly shut down the system:
Quit MAME and then restart it without the Legacy Recovery CD-ROM mounted. It should boot up into your installed System version: