I can't speak to the contract with DOE, though I'd encourage you to start using either one.

In my opinion the important thing is to use a software that uses EnergyPlus, so you can understand the functions within it. During modelling you'll have to refer to the engineering reference, and this will force you to learn about E+. You'll be able to adapt easily to either software once you have a handle on that, as they all use essentially pull E+ functions.

OpenStudio is free, so might be the better option of the two for learning purposes. Have fun getting oriented.