For a privacy friendly OS, surprised nobody has mentioned Freedombox

It’s designed explicitly for your use case, along with an easy path to other self hosted services. When you’re ready for more than it offers through the web interface, it’s a full Debian install under the hood - so you can install whatever you need to. Privacy friendly and super stable, with smooth upgrades to new releases and security updates for old versions several years after the new one is available.

As far as hardware, your old computer is probably more powerful than a Pi and can support more drives, but the Pi will be more power efficient. As others have mentioned, if you care about your data long term then backups are a must, so a separate NAS or a Pi with a large drive for backup storage is a good idea as well, whatever OS you choose.