I have a very similar commute; I live on top of a hill, about 600 ft elevation over 5 miles, most of the elevation change within the first mile.

I have a Surly CC. I carry a backpack with a change of clothes, laptop, shoes, and other small things. I keep my ulock and chain at work. In the first week, I was struggling. However, over time, although it is still challenging, I am getting stronger and don't switch to the lowest gear until the last 100-200 yards of my climb.

I find that using SPDs help immensely. Also, I have knobby tires and I wouldn't recommend it for streets.