Sending music around the house these days is becoming easier and cheaper, but often at very low quality. That isn't our interest.
Most plans we see involve one room where you want it to be good, with good speakers and a proper sound, attached to streaming to more rooms where the quality, although still decent, isnt the most important issue.
We start with Sonos. You can stream to many rooms at a reasonable price and can start with 1-2 rooms and add more later. There is now a viable alternative with BlueSound. A little more expensive offering better sound.
An amplifier and proper hifi speakers mounted on shelf or in ceiling can be £ 800 to 1600 and will play your music library from computer or itunes, internet radio, and also stream music from online providers such as Spotify/Tidal/Qobuz
Add-on rooms can be tabletop from £ 200-700 per room or amplifier and slim or ceiling speakers from £ 900 per room.
To add quality you need to start with a better source in your main room. This means Naim or Linn. Your quality room with Naim can start from £ 3.5k complete and go up above £ 7000.
With both these systems you can then add Sonos tabletop players for extra rooms very easily, and control can be by iphone, ipad, etc. to make it very simple to access and use.
To establish what is the right system for you a demonstration is a must. Only you can say what quality you are happy with and it is very easy to hear the differences and decide.
Let Which magazine pick your dishwasher but a music system is too important to leave to anyone else!
Here are some link s to relevant websites for you to check out:
Linn Music Systems made simple
All of these are easily integrated into a new or existing home. They can be added one room at a time with many combinations of price and performance. To build a template for your project we need to meet for an hour and take it from there