Several banks require you to have your account open for a certain amount of time before you can close it. They will charge you an early account closure fee, with an industry average being roughly $25. BB&T (NYSE:BBT) and Citibank both charge this fee if you do not keep your account open for at least 90 days. Other banks will require you to keep your account open for as long as 180 days. Make sure to ask questions about an early account closure fee before opening your new account, in order to avoid this fee.
Many banks charge maintenance fees, so make sure you know what the parameters are. Some banks require a minimum balance to avoid these fees, while others charge a flat-out fee, regardless. Typically, the minimum balance required is an average over the entire month, so if you do not get steady paychecks, you may need to ask the bank about this ahead of time.