If you own a domain, hosting Forgejo on a $5 Debian cloud server works perfectly for your personal use case. My site admin panel shows it's using 75MB of actual RAM (not allocated/virtual), it's truly very lightweight. Disk use is very low, just however big your git repos actually are is the key.
The internal SQlite database option is just fine, don't need to bother with PostgreSQL if you're only doing it for yourself (the DB only holds referential info, the actual git data is stored on disk in normal git directories). There's a built in backup command so you can build a simple shell script to run the dump command periodically and back up the entire thing to a tarball.
re: Codeberg, the only "downside" (not really) is they are for FOSS licensed projects only and frown upon using their service for your personal private non FOSS needs (they're not draconian about it, but it's part of the ethos the service is for FOSS licensed projects to use).
Suggestion: start learning git by using your
$HOMEconfig files as the first thing you learn how to manage; mentally easy to understand, low friction and just basic git commands needed. One of the most popular repo names we all use isdotfilesso you have plenty of examples to learn from: https://codeberg.org/explore/repos?q=dotfiles