I would go with 16GB for the kinds of things you listed.
If you don’t need a 3.5in drive then I would go even smaller to a mini form factor. It will definitely save you money on electricity. I think it’s the main choice here.
I would go for refurb, business line SFF machines. Something like ThinkCentre or Optiplex. Specific form factor based on drive needs but the smaller you go the more power efficient. I have one on the bigger side (internal psu) that runs about 12W idle.
Just double check that it can handle hardware transcoding. Should fit right in your budget!
I use Immich for sharing. Get some accounts set up for closest family so you can easily add them to albums. For others you can just share a link to each album, password protected or simply unlisted.
Personally, I run my internet accessible apps on my Hetzner VM behind a reverse proxy, whereas things like home automation, DNS and Octoprint I prefer to serve on my local network.
I’m running Immich on an old ThinkCentre with the default feature set. Currently looking at:
There is a bit more overhead for the control plane and cloud-native PG operator/backup pods but my instance fits comfortably inside a ~4GB allocation.