Just don't save your usernames/passwords if you bank on the browser, and make sure to tell any banking app to log out when you leave the program (you might not even be ABLE to stay logged in).
All data through CDMA cell networks is encrypted by default, not to mention the additional encryption that any reputable bank's website/app will have. As was mentioned above, online banking with your phone truly is the safest way to bank online.
In regards to rooting, it is only as dangerous as you make it. If you root and then grant SU permissions to "Swe3T fREE BaBEs 4 U" app, you're probably asking for trouble. But I only grant SU to Quick Boot and SetCPU, and other legitimate applications that don't ask for more permissions than they require. Just don't be an idiot and you'll be fine!