That is tough to answer. I am not in the twelve hundred dollar club but I can spend four hundred on three separate occasions and still feel good about it. I prefer to research before making a purchase but information overload can numb the brain fairly quickly.
Do you use iTunes? If so, you can stream from your computer to an AppleTV very easily. If you already use Windows Media Player, you can use a Roku and the Play To app. This also works for streaming from a smart phone, as long as it's logged into the same network as the Roku. I played with a Chromecast when they first came out, but had problems with it- I think it was my computer's fault. If you want to have music around the house and move the speakers as needed, Sonos works well, or the Yamaha Music Cast system operates similarly. I haven't used Denon's Heos, yet- I'm still interested in that.
A NAS would connect to the router- that acts as the traffic cop for the system and a NAS has a network adapter built in, so it's accessible to all computers on the network, as long as the network is configured to allow it. If you use IP-based streaming, I think you'll find that it sounds better than Bluetooth, but that will depend on the BT adapter. I tried a Music Fidelity Bluetooth receiver and it sounded good, as long as I wasn't comparing it with AirPlay through the AVR I was using at the time. Also, the range of BT isn't as great as WiFi and it's possible to extend WiFi farther, much more easily.
If you don't need radio, the easy way to do this is with IP-based speakers like Sonos, Heos, etc. Connect one piece to the WiFi and all of the rest connect to that to form its own network. You would download the Sonos/Heos/? app on your phone or tablet and control the music from there, using better speakers where necessary and smaller ones where it's only for background. These both have internet radio, so if radio is important, you're pretty well set. One thing you may not like is the fact that sporting events aren't always streamed online when the local channel is broadcasting and if you prefer the local announcers to the pinheads on network TV games, you could use some kind of AM radio with line out to feed a Sonos Connect or the Heos version. If you need more power for one area, the Connect Amp could work, but if you want a LOT of sound, a separate amp with more power is better. You can also use a Connect to feed a multi-channel amp if you plan to expand the distributed speakers and possibly have a volume control for each area/set.
This is all expandable, so you can start small and build as you go.
If you need the receiver because you want to use several sources (CD/DVD/BD/Cable music, phono, etc), you don't need anything special- as long as it's decent, noise-free and has enough inputs, you can feed the REC out to a Sonos Connect/Heos and use that volume control instead of the one on the receiver- doing this eliminates the chance that someone will turn the volume down on the wrong control and cause a lack of output and the confusion that goes along with this scenario.
