The average yearly price of a checking account at a bank can be as high as $200. For each bank that you're considering, take a good look at its fee schedule and think about what you're likely to spend. On the other hand, remember to include interest rates in your calculations. A higher-fee bank may offer competitive interest rates, so if you're also planning to save with that bank, you could offset the costs considerably. Don't let an unattractive fee schedule make the decision for you -- it's not the whole story!
All banks assess maintenance fees, so make sure they're competitive for your kind of account. "Free" checking can get rid of the maintenance fee, among others, but the key is the specific conditions, which change from account to account.
As far as ATM fees, just keep in mind your actual behavior. Some younger banks, especially online banks, offer rebates on "foreign ATM" fees. If you travel a lot and need cash on a regular basis, you should definitely rate banks higher that provide this convenience in one way or another.
Returned checks and insufficient funds (NSF) fees are a great way for banks to make money, because they're counting on those mistakes and oversights that happen to us all from time to time. Don't plan to pay these, but do look into overdraft protection programs at each bank you're researching.