Hope this reply isn't too late.
I am doing something similar to a house I have just bought at the moment.
I am running AT LEAST 4 runs of Cat 5e to each room (8 to key locations). You would be amazed at how versatile this cable is. It can be used for almost any purpose. By using Baluns you can transmit audio and video over it. I will be using it mainly for network connections (yes I have wireless at the moment but you can't beat a decent cable
)
Personally however I am also running lengths of component cable to each location for visual and speaker wire for audio. (Make sure it is good cable though).
All this will run back to a central location. In this location I will have all the sources (2 x Sky Boxes, DVD player, Media PC, and all the amps needed etc). which all run through a Matrix Switcher (something like the neothings) . This will also the user to view any source in any room using a couple of decent RF remote controls.
For HD what about running HDMI/DVI cables throughout.
This multiroom stuff isn't cheap when yuo get into it and I am doing it the relatively cheap way. If they want wall mounted controls etc. 15k is easily spent. You could easily spend thousands on cable alone. As for why they want 3 x TV sockets???
Co-ax is appalling. I have put one run to each room just in case all else fails but there is really no need to be using it.