I think Sheppard would be an unashamed eighties fan. I also think that Rodney (having given up piano at a young age - is that canon or fanon?) would either completely shun music altogether, or have a closet love of off-the-wall modern composers like Arvo Part or even listen to weird sounds like variations on sine.

Ford would like whatever's in the top 40. Elizabeth would be conservative and listen to whatever's on the public stations.

:-)