This all depends a lot on:
1) How many simultaneous playback sessions (several users play several files simultaneously) there are at your home at the very maximum and
2) whether the content you serve from your large media library is mostly in native MP4 containers (H.264, AAC audio) or if you need to do a lot of transcoding in parallel
If you're going after lower power and physical footprint, you should consider buying an Intel NUC (http://www.anandtech...for-enthusiasts). The NUC5I5RYK has a Broadwell-U, which only has 15W TDP, which is an Intel mobile CPU optimized for power usage. There will also be another Intel NUC coming (http://www.pcper.com/news/General-Tech/New-Intel-NUC-Will-Feature-i7-Broadwell-U-CPU-Iris-6100-Graphics), which has a higher 28W TDP CPU and is also specced a bit higher.
These NUCs should easily handle several Direct Streaming / MP4 remuxing sessions, if the content is in a native format. If the content needs to be transcoded, and should you decide to buy a NUC, you can also use Intels QuickSync, which will barely use your CPU at all, which means that is also saves a lot on power.
All playback (decoding) and transcoding will be accelerated by QuickSync and it is supported since the newest Air Video HD releases (http://forums.inmeth...ed-transcoding/). Currently, there is a limit of one transcoding session that can be hardware accelerated though, multiple session in parallel will use the CPU for the remaining sessions. QuickSync still is a bit lower quality compared to software decoding though, so you need to test yourself if the quality is sufficient for you.
There you go.