Some banks are free to use as long as you keep your account balance in the black, while others nickel-and-dime their customers with fees at every turn. Even small fees can add up over time and eat into your account balance, so look at a bank’s fee schedule carefully and make sure you understand what you need to do to avoid them before you open an account there.
This advice holds true even if you sign up with a bank that advertises free checking; there are always fees somewhere. You may encounter fees for letting your balance fall below a certain threshold, not having your paycheck directly deposited to your account, overdrawing your account, using an ATM, requesting paper statements, and even closing your account.