I buy stuff with credit card over the web on a PC all the time. I don't even have up to date antivirus software on my PC. Never had a problem.
Make sure the web site is their web site and not from some link you got in an email that looks a little different. I think most internet CC fraud is a result of phishing. People send emails all the time posing as your CC company or a merchant and give you a link where you need to provide your CC information for some reason or another. Never ever trust these links you get in emails. Always navigate to the web site by typing the URL in yourself.