Hey, welcome to the concept of self-hosting! This is where I was 15+ years ago.
Realistically, I'd just recommend installing something and trying it out. You'll iterate many time before you'll slowly start to align somewhere I suspect, in terms of software/approaches etc.
If you want the very first steps, then why not simply connect your old PC to a monitor and install a Desktop version of Mint? It's super-"wrong", but it'll get you started. Once you reach a stage of not wanting to waste memory/CPU on a graphical system, you'll be able to do something like systemctl disable lightdm.service and voila, graphics don't load on start anymore. Once you get even more confident, apt remove gdm3 xfce4 xfdesktop will remove any extra disk space (I'm dropping DE names that I approximately remember off the top of my head). With the packages for graphics gone, your system is indistinguishable from a server now.
Overall it's a nice path to walk, or at least it was fun and somewhat educative and very frustrating and giving a sense of control for me personally. Do you have any specific questions?
