I'd suggest buying something like the Netgear Ultra 4 or Pro 4. These are 4 bay NAS which you can buy with either no drives or a combination of drives. It has redundency built in so you have protection in case of a drive failure. It uses 1 drive for redundency, so if for example you bought an empty unit and put in 2x 1TB drives, youd have around 1TB of storage. If you had 3 drives, youd get 2TB storage. It is also very flexable and expandable. Just add in another drive of the same size and it will expand automatically. If you ever fill up the NAS with drrives and want to expand, just replace the current drives one at a time with larger ones and let it rebuild. When its finished with the last drive, it will then let you expand to the increased capacity. The idea being you can just keep on growing with it later. I've been using these for years, with a NV+ before that. The NV+ is too old now however. They currently support drives up to 3TB, so you can put 4x 3TB in for a huge 9TB of storage if you need that much. They should soon support the 4TB drives as well. If 4 bays is too big, you can get the 2 bay version as well, this works in the same way with 1 drive for redundency.
The netgears also have a nice set of media servers built in (uPNP, DLNA and SqueezeBox) and lots of apps you can install for other things. I'd have a look to see what you player supports and/or if theres a specific app for it on there or if it will use one of the built in ones.
I use one of these to a Logitech Squeezebox and it works very well playing my FLAC collection.
Netgear seem have gone all windows-8/tablet style on their website, made it totally useless and I can't even find the Ultra or Pro anymore. It seems they only want people to find their
ReadyNAS 100 series, which I have not used but I would expect to probably be similar. I hate it when companies do stupid things with their websites.
I would also suggest you use a gigabit network however, and maybe get a separate switch instead of plugging it all into the router (unless its gigabit). The audio wont need gigabit, but having the network at that speed should be enough to ensure other things like file transfers to/from the NAS don't interfear with your music playback. The main difference between the Ultra and Pro version is that the Pro has the ability to team or bond the network ports for increased throughput - you wont need that for music, I have it because I put HD uncompressed video on it as well as music.
Another brand would be QNAP, they tend to be more expensive. I think WD have also recently introduced a NAS box, that might be worth looking at as well, but I've not tried one so cannot really comment. One thing to note is that a too low-end CPU in the NAS will hamper things when scanning a very large music collection, that might be part of the problem you have now.
I'd also second the comment about wireless - don't use it for streaming, its far too unreliable and is not worth the hassle, I use a cable/wired connection for everything, far less hassle and 'just works' whenever I want it to.