First, realize that you are not selecting an API report date. Instead you are giving the detailer an idea of your preference. He will fill his quotas first, and look at your desires as a distant second. I had initially requested a fall report date, and I ended up having orders to report a little more than 2 weeks after commissioning.
That said, I found that it was a major advantage to be entering the API pool in June, as opposed to later in the summer. When I showed up in the pool, there were only 50 other people waiting to start. When I finally classed up a few weeks later, the pool had climbed into the hundreds. There are still friends that I graduated with in May 2006 that are still waiting to class up for pilot. In my opinion, if you are looking to get through the training syllabus as quick as possible, you probably want to get to Pensacola as soon after commissioning as possible.