Now that you know a little bit about how banks work, let's go over the key features you want to pay attention to when selecting a bank account. You can use Google's site to compare some popular checking and savings accounts.
Like credit cards, you will have to pay attention to a certain rate when looking at savings accounts (although some checking accounts have one at times too). This is your interest rate that you will be earning on your balance with the bank. It is called an APY (annual percentage yield), similar to the APR (annual percentage rate) on credit cards. This number is typically around 1% for savings (but there are some banks who offer something like 0.35%) and next to nothing for checking accounts nowadays. Normally, the savings interest rate is much higher, but the government is currently keeping interest rates low to encourage consumer spending. And obviously, the higher the APY on your account, the better since you will earn more interest.
One minor thing to keep in mind is how often your interest is compounded if the bank you are looking at is advertising a higher interest rate but does not specify that it is the APY. Compounding is the magical way of earning money exponentially since your interest earns interest, then your interest's interest earns interest, and then... well you get the idea. Of course, it takes a while for this effect to become significant and almost all banks compound interest daily. The APY is calculated as the effective rate using a compounding period of one year, so it should be a good comparison tool across banks. You may be interested, however, in how often the the bank pays out interest as well (most pay out monthly I believe).
Another major feature to pay attention to is a monthly fee. Sometimes, banks charge a monthly fee on your account unless you maintain a certain minimum balance. If you are about to open an account and they mention that there is a monthly fee, I would ask first if there are student accounts available. Most of the time, these accounts don't have any monthly fee or any requirements. One such bank I know this case applies to is Bank of America. Make sure to avoid paying monthly fees on either your checking or savings accounts, simply because there are alternatives out there which don't have such a fee. There may be other fees such as an overdraft fee and other fees that you should look out for so make sure you read through the fine print.
The last feature to pay attention to is the minimum amount to open an account. For checking accounts, this is usually either $1 or $100, but it can vary. Savings accounts usually have slightly higher minimums to open, either $100 or $500. Obviously, you have to make sure that you have enough money to put into the account to open it.
I will mention some of my recommendations for checking and savings accounts in the next post.