In my grad program, we spend the first year in rotations and classes. Before the start of the second year, we are expected to join a lab. I found it difficult to prepare a great application package with all of my first year responsibilities and halfway through the NSF application, I just stopped. I put all the materials away and waited for the next round. In your second year, you have a better idea of your project and will likely have a stronger research proposal (and more to say on your personal statement). Since the 3 essays you write for the NSF should be cohesive, it was the best decision I could've made for myself at the time. I was fortunate to have been awarded the NSF and I feel strongly that I wouldn't have been selected the previous year.
After I prepared the NSF application, I more easily applied for the NDSEG the same year (haven't heard back yet). The NDSEG application is more straightforward with less mental obstacles on the application, but no less competitive. I see no reason you shouldn't apply for both in this sense. Didn't apply for the DOE.
My advice is if you have a strong enough application, swing wide and go for them all! Ask someone to review your materials (grades, GRE scores, research activities) before you start the application process. Good luck!