You can get an old Optiplex micro PC (Optiplex 3060 Micro for example) for around $100 or so online for the time being. The drawback with these, a NUC, and the Shield is that there’s nowhere to store HDDs and you’re forced to use USB rather than SATA. As your collection grows you’ll almost certainly want a larger case to house multiple HDDs rather than having 10 external drives cluttering your space.
I went with a Fractal Design Define R6 for mine which can hold 12ish 3.5" drives in a relatively small footprint.
Also if you want to try Jellyfin you can run it alongside Plex. You don’t have to choose one or the other. I’ve been running Plex and Emby (what Jellyfin was forked off of) for years and both work fine but Plex is more feature rich (with the Plex pass)