Nick, adding a NAS to your home network is extremely easy, it's basically just plug it in and name it, then it just works. There are many good NAS products available now. Read some comparison reviews to decide which NAS is best for you.
Now if you are talking about running LMS right on the NAS server to avoid a computer, I don't know about that. I did that in 2007 and still run an old slimserver on my ReadyNAS. It was cutting edge when I first did it, but the updates had to be compiled for the NAS, which was always slow, so bugs lasted far longer than they should have. My NAS had too slow CPU for slim and only 500KB memory. Modern NAS like
this have more CPU and memory, but the software is bigger now. I think you'd be better off getting a real computer, like a Zotac silent PC with Win8 for a couple hundred, then use a NAS or SSD USB drive for the library.