Thanks for the info so far guys.

I am a beginner right now, but I have an entire year to get into shape for the commute. Which makes me think like chinarider mentioned, the speed gains level off.
My goal is to do the 35km as fast as possible. Because of this, I am not trying to get sprinting speed up. I think it's too long of a distance for that to help. I suppose your right that average speed isn't really what I'm looking for either.

After analyzing my route more, and looking at what I'm dealing with, it seems like the thing that will improve my time the most is my ability to climb hills. The hills aren't too steep, so I just need the stamina to maintain usual cadence on a medium to low grade for a while. Obviously I also need the strength to pedal at 80 rpm on a hill as well.

Will intervals help with this? Is stamina for hills built the same way as stamina for flat roads? In other words, I know long riding at your regular pace will improve your stamina and endurance for longer rides. But will that carry over into helping me get up hills faster, or will I need to do something else?

Thanks for the help so far guys I'll definitely look at getting some good reading materials as well.