I know in my class, most people moved in 1-2 weeks before school started. I moved a month before school started, but I was already in San Antonio, so I was just re-locating closer to the medical center. Depending on where you are going to school, I would plan on moving about 2 weeks before school, but already have your apartment and lease signed and ready to go. Don't wait to look for an apartment 2 weeks before school starts. Moving 2 weeks before school starts will give you time to get cable and internet hooked up, call the electricity company to get the bill in your name, etc... and plus, you don't want to be all stressed out right before classes start. This will give you some downtime.
The apartment complex I went with allows only a 1 month booking of an apartment in advance if there is a wait list. I can't imagine apartments would do any longer than that, because if there are other people on a list ready to move in, they will do that, otherwise they are losing money.