Many registrars let you buy a domain and set up dynamic DNS for it within their system so you can own a domain and get dyndns on it.
Otherwise you could accomplish it with a VPS but you’d only need the smallest one available because it would just need to run nginx to forward to your home ip (and a small tool to update that IP when it changes). So you could probably get something for less than $5/mo.
I run Debian on most of my systems and run all of my services in docker (with rare exceptions for node_exporter or stable core tools). My base systems get automatic security upgrades, and then I’ll manually check in every few weeks whenever I feel like it.
My services in docker are version locked to a specific major version (when there’s a tag available) so I can usually re-pull to get minor version updates freely without breaking issues. My few more finnickey services get manual upgrades from me every 6 months or so only.
I usually stick to an OS version for as long as I can, and to that aim I stick to LTS versions with long support windows.
4 major versions in 12mo is…a lot. Especially if those include breaking changes for you. Yikes