Lots to consider, but quick answer :
Node0 home-running sounds fine ...
power & lighting could be done likewise ...
Cat-6 will cover Gigabit Ethernet ...
and can be used for other things ...
CT100 cables (co-ax) can have terminals that split-out DAB & TV & FM from one cable ...
Sky can need three cables (depending on what you're going-for), especially if the box isn't in Node0 ...
running more cable costs little extra ...
so - as a quick answer - I'd be tempted to go for a minimum of 3x Cat-6 + 3x CT100 to each location ...
and power & lighting, all radial to Node0 ...
NB: keeping power & signal at least 100mm apart is a good idea ...
HTH
Chris