Hardware Advice

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I used an OptiPlex that's likely the same exact model as a server at one point. It works, but any transcoding at all was pretty much a no go. So if your media is 100% compatible with client devices, that's fine. If not, you'll need something way more recent (iX-8yyyy+).

As a curiosity, why would you set up a new server rather than revise libraries and provide access to your own with either a reverse proxy or VPN setup? The i3 or a newer one you mentioned could either work as a HTPC, or you could use a client they already have. Managing one server will prove much easier over time, even if you're able to access theirs remotely. If you're a student, then....yeah I get it. You can't really run a full-fledged server on campus wifi (and not get caught).