Typically I usually make my way to Riverwood, then I go to Bleak Falls Barrow. This gets me some gold for the Golden Claw quest and I get Farengar's quest out of my way while I'm at it. After that I normally do the 'Dragon Rising' quest for Balgruuf. That's a typical beginning for me.
Lately however I've been going straight to Solitude/Windhelm for the Civil War, and a few times I've visited the Companions for work and quick leveling. I just have no motivation to do the Main Quest, as I do not care to use Shouts. I like rebuilding the Blades, and that's it!