I haven't read the books but this series is more fun if you root for the Lannisters. The Lannisters seem to be the only familty with the military and political skills necessary to win. Tyrion, Tywin, and Jamie all have their vices but excel at what they do.
The other possible side to root for would be Daenerys who is quickly showing she may have the ability to stand up to the Lannisters.
While the Starks were the noble choice to root for they quickly showed they are completely out matched by the Lannisters and seem to have come to an end.
So my advise is to root for the Lannisters or Daenerys. It's like watching Jaws and rooting for the shark - you'll be less disappointed.