Low cost home server setup for Jellyfin (expandable, 4K direct play)

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A few things here: mini PCs with newer-generation Intel processors can be a good option. So can old workstations like Optiplex machines. However, these are not expandable unless you get another device to run your drives. Additionally, I don't know whether your dorm will monitor network traffic, but you're asking a lot to sap 60 Mbps of upload + more locally. That's not likely to work very well. If you don't need transcoding (spoiler alert: it will definitely happen, so be prepared to explain why things don't work) you can skimp a little bit on processor generation. Keep in mind that the more you cheat now, the less future-proof your server is later.

Most recent-ish machines with a decent network card (10/100/1000) should work fine, but again, you're very unlikely to get that sort of upload speed. Even locally, depending on client, streaming 4K (remux) can be problematic due to peak bitrates not matching average (duh). Trying to find something within the last few generations of Intel that supports QuickSync will allow you to utilize that machine for much longer should transcoding be necessary.

My current server uses a Meshify case with like 11 bays for 3.5" HDDs plus two more mounts for 2.5" SSDs. Super easy to expand if you have the hardware to hook it up to.

https://www.fractal-design.com/products/cases/meshify/