I need help getting this all to work?

Ok I am only 50 but am so lost with all this new stereo lingo and products. I have a family that wants to listen to music stored on a computer and also be able to listen to Apple radio. I don't want a simple bluetooth speaker. I used to have quality audio equipment and want to get back into listening.

Here is what we have:
3 MacBooks
1 Mac full size computer where ripped cd's (300) are stored
4 apple TV's I think 3 version
Apple airport older version
Apple Airport express
4 Iphones 4-6 versions

Want to have
 
Integrated amp like Hegel 80 and goo speakers 

Want to be able to

Have wife or 12 year old simply play stored music and Apple radio by pressing play and choosing source. No fiddling, no turning on 5 components, little to no drop out, no hassles.

The choice of speakers/amp are a personal choice so I am looking to do that separate unless there is a product such as the Hegel that might eliminate an extra needed product.

Budget besides the above is approx $5k .

I appreciate any help and direction as to how to get this going. I have read and read and think at this point I am confusing the situation even more. Do I already have everything besides amp an speakers?

Thanks