I couldn't get the low voltage Xeons for a sane price in Germany, so I settled for a second-hand i3, which turned out to be more than enough for what I'm throwing at it.
I'm running ESXi as a hypervisor managing two Ubuntu VMs at the moment: a router and a fileserver managing two volume groups (6 TB dump storage for movies, music, etc. that's not too important and thus unmirrored, 2x2TB mirrored storage for photos and other important data that should not get lost). Thanks to the two network ports I can completely isolate the fileserver from the open internet as only the router VM has access to hat port. If I want to access my stuff from outside, I can VPN into the router and thus have access to the fileserver.
The next points on the list is Plex or something similar so I don't have to manually re-encode movies when my TV doesn't like the audio codec. Here, the i3 might struggle a bit, but we'll see.
As for the cost: I spent 200€ on the server itself, 88€ on 16GB RAM, ~20€ for the SSD case and power adapter cable and ~65€ on the SSD. The i3 was ~25€, so I'm up to roughly 400€ for the entire server (plus storage costs, but you'll have those anyways). Compared to what you'll get for that price it's an absolute steal, especially when you compare it with several "low budget"/homemade NAS builds floating around the net/youtube.
Bonus points: you can stack them on top of each other.