I keep all my critical files on my NAS, accessible from any of my machines at any time.
That NAS has a daily local backup via external SATA drive, and a daily network backup on a second NAS on the other side of the house.
My primary NAS is a Synology DS413 4-drive model, although I currently don't have 4 drives in it. I run each drive as an independent separate volume, which makes managment a lot easier, and keeps speeds high. My multimedia is housed here, as are my critical files.
My secondary NAS is a Synology DS211j 2-drive model. It acts as my surveillance camera recording drive, as well as the backup for my critical files on the DS413.
If you want a Synology NAS for multimedia playback, one consideration is to get one that does transcoding on the fly. However, I didn't bother because I'm told it doesn't always work perfectly, and more importantly, most current portable devices can handle even high bitrate video these days. My iPhone has no problems playing a 10 GB MKV file.
I think more important is the read/write performance. For that you need a fast CPU. Luckily, in 2014, they have the DS414j for a 4-bay model, which includes a dual-core ARM Cortex A9 at 1.2 GHz. It also has a decent 512 MB RAM which is good for OS performance, and USB 3 for fast local backup.
For your usage otherwise a DS213j would suffice, but it only has a single-core CPU so performance suffers a bit, and it doesn't have USB 3 or SATA for fast local backups. That said, USB 2 is OK after the initial backup, since subsequent backups are incremental.
These do have AFP and Time Machine support, but I don't know how well that works, since I never use it. I back up my computers locally. I don't have to do it all that often either because my critical data is on the NAS anyway.