Since you have no proof of his US citizenship until his US passport is approved, I would wait to apply for his driver's license until the passport is in your hands. Explaining the intricacies of US immigration law to a DMV employee will not be a pleasant experience; perhaps they could hold open the application until you are able to show them proof of his US citizenship, but either way I'm sure they won't just give him a licence and take his word at face value that he is a citizen (even though he is).
Passport -> DMV is the order in which I would do it.
You should also prepare yourself for the post office employee to be equally unfamiliar with the Child Citizenship Act. I would go armed with a print-out of the section I cited above, and be prepared to explain why your son has now become a citizen. Be aware: the post office does not hire people for their intelligence, so you may need to speak slowly and with easy to understand words until they get it.
I hope it goes smoothly!
If the son became a US citizen under the Child Citizenship Act (2000) then an N-600 is not required. You can apply for it, but it is purely voluntary. You can jump straight to a US passport if that is your wish.
http://travel.state.gov/visa/immigrants/types/types_1312.html
If you wish to obtain a US passport for the child, follow these instructions: http://travel.state.gov/visa/immigrants/types/types_1312.html#7
Autumnal reacted to Hypnos in Legal Resident AND US Citizen. What to do when on the limbo?