The key to when to apartment hunt in Charleston depends on why you're moving to town. If living anywhere in the city is an option, then you only need six weeks or so to find a place. If you're looking for a place with easy access to the University though, looking in April or May is your best option.
Charleston is a small enough town that you are only going to get so many chances to find an apartment. Make sure you treat every meeting, email and phone call with prospective landlords seriously. It may be your best and only chance to find an apartment.
Public transportation is not available in Charleston. This limits your options. If you plan on staying close to home, you can commute around the city itself and to the university and back fairly easily on a bicycle. If you foresee needing to visit surrounding communities like Mattoon however, bringing a car is a better option.
A Panther's game at the University is the quickest way to see the pride that this small town takes in it's school. If you head downtown, you'll be treated to century old architecture and restaurants that feature local flavors. Lake Charleston is a wonderful place to relax with friends and to get to know some of the other locals.