I have been playing with various Linux distros with the goal in mind of
having the smallest possible (in terms of disk size) install of WordPress
Last I tried was VMWare Photon and a WordPress docker image with DB.
At the end it ended up at nearly 4GB in total.
Turnkey with WordPress was a tiny bit better.
I do think it should be possible for sub 1GB in total.
(Then I could launch a lot of them on a vmserver with strong isolation)
You can try a Debian base image but you would have to manually install Apache and MySQL. I think the biggest issue would actually be with MySQL as it requires a lot of space on its own, not including the database size.