I've been using a Synology DS212J (few years old now), on which it is very easy to install LMS - click and go basically, via the Synology DSM web interface. And up until last week I was using my SBT as a 'player' either via ethernet or WiFi, plus iPeng on the iPhone as a 'remote', or the LMS web interface. No need for a laptop, plus if you run the NAS in RAID mode - you get redundancy if one of the drives fails. Worked well for me for years.
The other good thing about using a NAS is that you have forward flexibility - you can ditch LMS if you like and use just any combination of kit + streaming software.