I fly either Delta or AA, and I generally start looking at the prices as soon as they're available to search. Then when it goes down, I'll book the tickets. One thing I have noticed with Delta is that if you select main cabin, you *may* see a better price for Delta Comfort or even first class than was originally shown on the first page of flights/prices when you reach the next to the last screen. It's not always a given, but it has happened to me a few times so I thought I'd mention it. That's booking through the Delta website, though.
Happy trip!