Keep in mind that banks are always required to notify you of the fees for their accounts. The best account to choose is usually the one with the lowest fees, regardless of the interest rate.
Keep an eye out for potential extra charges when shopping for checking accounts. Ask about monthly fees, check processing fees, and ATM fees. Also be wary of cost-free checking accounts, as the bank may charge you if your balance drops below a certain amount. Also, the charges for printing new checks can often be much higher at your bank than through an outside printing provider.
In this day and age, it doesn't really benefit you to put money into an old fashioned "passbook" savings account. Often monthly account fees overshadow the small amount of interest you will earn. Instead, put your money into a checking account. If it is a larger sum, look into a money market account. In this type of account you will earn more interest than in a savings account, but watch out for additional charges if your balance drops too low.