The quetion is way too vague. What do you mean by "best" checking account? There are different types of checking accounts catering to different needs of different people in each bank. For Eg: I opened my free BOA Checking account 5 years ago and it was free. I used to be a student back then. 5 years on, it's still free. Then I was lured into opening a Chase account as they had a promotion going on. Meeting the requirement of setting up direct deposit of more than 500/paycheck for the first 6 months of opening an account would mean I'd get 200 bucks deposited into my account. I closed the account after 6 months as banking with two separate banks was unnecessary back then. I started banking with Chase again as I had various Credit Cards with them and they also had a promotion going on again, $150 for same terms and conditions. 

So it all depends. Some banks offer free checking accounts. Some don't. More often than not, banks are more lenient towards you when you're a student. Else, most banks will charge you monthly fees.