Jellyfin doesn’t seem to be as oriented towards music but will also work and many people use it for music

I buy music from Amazon music, hd tracks or band camp it’s all drm free and put it on my server behind a subsonic based server . That’ll give you the closest to a streaming service. Otherwise just sync music on your phone old school.

Would not recommend under clocking. Buy a kill-a-watt measure your idle that’s your general power usage. A cpu that has a low TDP and newest generation is going to be the most efficient. After that it’s each item you add adds more usage at idle which is going to be most of your time. Transcoding efficiency doesn’t matter much since you are likely not transcoding when you aren’t watching videos. Have an appropriately sized power supply that platinum or gold certified, usually the extra cost will be justified by power bill usage over a year or 2.

For example my older gen server, a dell r720xd, sits about 120-130 watt but with 9 spinning disk drives each about 5w per hour it sits around 200w per hour. This does go higher when watching videos but is far from the average. 200w per is roughly $15-20 per month where I am located.

I hope this helps.