Id say rip blurays on your main PC/laptop and build low power device for server.
Streaming musing and sharing photos is not intensive task, but streaming 4k video is another storry. Unless you need 4k streaming you should be fine with almost any intel cpu that supports quicksync and with no gpu afaik. I googled that Lenovo and it seems like it has Xeon E3-1226 v3 which does support quick sync, so I bet it will run just fine. My celeron g3930 can transcode 1080p