About online banking risk?

hi friends!! I have to order some commodities online and have read much about the risk of online banking. i will be paying the party the money directly from my bank accnt. i have seen on the internet and many movies that when we do this banking online the username and pword or cardnumber is stored in the computer and can be retrived by hackers. i wanted to know that where are these stored in the computer. I clean my history and saved pwords, cookies from my computer. is there any other place this information stored? f i know it i could clean even that.