I wouldn't worry too much about it whichever way you decide, there won't be much of a crowd that early in the morning. The area doesn't open until 5am, either.
When we travelled in December, I did the online checkin and prepaid for the checked bags, checked in again at the kiosk, and again at the desk so that the agent could see our passports and tag the checked bags. We then took our checked bags to the x-ray area, gave them the bags and waited for the agent to say the bags were accepted. Then pick up a customs form and fill it out before getting in line for security. In the line there is a randomized process for passengers to be selected for extra screening, always dodged that one! Go through security, collect your carryon items and go to see the customs agent and then you're done! It's very efficient and in a relatively small space.
If you have bags to check it is cheaper to purchase that online from Continental when you do online checkin.