Well, the problem with doing pop music is it dates fast and ties your series to a certain era. How many different forms of pop music emerged in the last century? Which ones will still be big in the 23rd century? Will they have been replaced by different forms of pop?
I think the last is most likely. We'd see new pop, new instruments and wholly new ways of looking at music and it's sort of impossible to try and predict how.
Classical music, however, well, it's been with us for centuries. It's not unreasonable to assume it'll still be with us a few centuries from now. It's basically the safest bet for any future society, particularly as the use of classical music also won't date your show.
I would have liked more modern and experimental classical music on the series (in another thread, I observed I really liked the touch of Philip Glass in BSG), but you could argue that's liable to pretty much the same problem as pop music: What if any of it will stand the test of centuries like the rest of the repetoire has done?
Oh, and electronic music is sort of a sci-fi cliche, and we don't even know how many of those early electronic instruments will still be used
centuries from now - maybe they'll have been replaced with more complicated machines or something.