From top of my head:
A- If you want to be able to restore to any point after installing your system: LVM/ZFS/BTRFS snapshots got you covered.
B1- If you want to install your system the way you want, you have Kickstart (RedHat family) and Preseed (Debian family). You can provide an installation template to the installers, and they install your system the way you want.
You want to get your /etc/ afterwards the installation? Either provide it on a disk, or your local network, or anywhere on the internet. Either integrate it to your Kickstart/Preseed end hooks, or do it after your first boot.
B2- If you want something more fancy? Create a FAI installation media which installs the system you want.
C- You want to transform an existing Debian system to something you want? You get the dpkg package selection state and set to the target system, apply the state so the system is converted to your own selections. Apply the /etc via git or any way you want.
D- Want something more programmatic? Run an Ansible playbook locally (This is how GitLab installs and configures itself during install).
E- For fleet installations there are XCAT and network variants of B1, but they are out of scope for personal systems.
We use E in our system room. I used B1 for personal systems and B2 to deploy an installation country-wide via USB sticks. I used C in the same project for a small subset of servers. In these cases, all systems are operational in the first boot, starting from a known state.
I know a lot of people using A, and nudging me to try/use it. GitLab uses D every time I upgrade it.