Their are many good banks that will give you a checking account. I would check different ones as they all have different rules. Read the agreement very carefully before you sign it so you know exactly what you are getting.
If you are International student and want to open a checking account you should consider account for Non-U.S citizen with is free checking account you can open in any bank tell them that you want account for student not standard account, they will waive montly fee!
If you are international visitor, open a account as temporary visitor the best option with be free checking account with a debit card so you may shop online, withdraw money from your banking account or shopping! hassle free
Why you don't consider to Open account in Poland and use the same account International, I have a friend from Poland that have account free checking account with passbook and check that he can use here, even debit card working AMT machine!