Jellyfin: The Free Software Media System

Make sure the clients can play the media without transcoding, there are lists of formats Jellyfin support natively but generally speaking H.264 in a .mp4 container is a safe bet and pretty common to find. If your files aren't in that format then you can quite easily remux them, and add some automation to it so it's done ahead of time. The Pi can remux files but it will be pretty slow so best is if you can have another computer do that part.

Oh yeah, if Jellyfin insist on transcoding it might be due to poor / shaky connection such that it wants to transcode to say 480p / 360p or something and then best is to try and turn it off completely in settings.