One thing that I have learned recently with regard to American in particular is as follows. If you book MAIN CABIN, if the price for your flight goes down, you can get a flight credit for the difference. NOT a cash refund, but a flight credit. The credit is only good for a year, but if you fly on AA fairly often, it's a good deal. Recently we were able to get a $150 credit for our upcoming flights to St. Croix. Main Cabin costs more than economy, but you get a seat assignment included. You can also book Main Cabin Extra. That costs more than Main Cabin, but if the price goes down, you can get money back to your original form of payment, as compared to only AA flight credit.
SO--to address your original question--I would check prices as soon as possible and book Main Cabin, at a point where the price is acceptable to you. Then do an automatic price check online and if the price goes down, call and get a price credit.