Personally, I don't think there is a "best" web browser. It's all a matter of opinion and personal preference, as all web browsers perform the same basic functions pretty well.
That being said, I would have to say my web browser of choice would have to be Google Chrome. It's fast and secure, not to mention that all my bookmarks are in Chrome. However, sometimes certain sites (such as ones that use the Unity Web Player) don't show up properly in Chrome so my backup browser is Firefox (which is usually just as fast and secure as Chrome).