The issue will be accessing and choosing the music on your NAS drive so that comes down to the app on a phone/tablet to do that. From there, all you need is a bluetooth speaker of which there are many in your budget.
Trying to scroll through albums/tracks on a NAS drive is tricky on many devices including fairly expensive "transporter" type devices, so I'd stick with using your phone as a remote and streaming via the bluetooth on that. Makes it much easy to choose the next album etc.