Yeah, I might join the Companions, then go north to Winterhold and join the mage guild. Do a few quests, then come back down to Whiterun, kill the dragon and get Lydia.
I think it's safe to assume that the actual MQ starts when you killed that first dragon for the Jarl of Whiterun. I mean you don't even know you are the Dragonborn up to that point and neither do the Greybeards - they only shout your name after you have absorbed your first dragonsoul. So I also plan to rise to the leadership of the Companions, wipe out the Dark Brotherhood and get myself a name in Skyrim before I add the burden of being the Dragonborn to my character. 

