I haven't *rushed* but I did just clear normal, spent about 4-5 hours per Act doing every little bit of exploring and clearing possible. Also reset Act 2 due to an overzealous text skipper in my party.
I am a firm believer in experiencing the story first, then mindlessly grinding the game. Now that I have truly come to understand that the changes to the Diablo system make it a lot more about skill than simply numbers (i.e. D2) I am far more pleased with my time learning the complexities of my class than I would have otherwise been.