Most legitimate internet checking accounts are safe to use. As with any site that processes personal information, just make sure it is a secure site by checking the beginning of the website address for 'https'.
There will always be risks to using the internet checking account but you just need to make sure you follow all the safety measures and make sure you are covered if anything is stolen.
There are quite a few banks that offer free internet checking accounts. These include TD Bank, First Bank and Bank of Internet. Check to see who offers the most features that meets your needs.
HSBC does indeed offer free checking accounts. With any of the checking accounts offered you can use the internet banking online with ease. They make internet banking very easy.