Firefox is the most secure browser after Google's Chrome.
The convenience and the security of the Firefox browser comes from the continuous development by the open source developer community and a vast number of intelligent plugins/ add ons that are developed for Firefox browser. Needles to say that if you are an adventurous person you can't settle less than Firefox browser as your favourite browser.
The plugins and add ons need a special mention. I have written separately about them. But to mention a few , most essential and basic add ons would be NoScript and WOT browser plugins.
If you are an Internet explorer user, which most probably you are, then I would definitely ask you to try Firefox browser. It is way much better and convenient than Internet Explorer.
You can download firefox browser from this link