There are four main types of browser technologies these days. The biggest one is the Microsoft Internet Explorer family of browsers. Internet Explorer comes standard with windows (unless you are in the European Union). Internet explorer is the most exploited browser by hackers, partially because it has the most market share, and partly because of its use of ActiveX objects. If a user is careful and practices good browsing habits, Internet Explorer is as safe as the rest. I recommend all windows users at least have this installed because there are plenty of websites out there that require you to use it. Microsoft is notorious for having their websites only work in Internet Explorer.
The next most popular browser out there is Mozilla Firefox. This is the successor to the Netscape heritage and is overseen by the Mozilla foundation. Firefox was the first browser to incorporate a system for third party vendors to develop extensions and add-ons for it. There are almost two million add-ons for Firefox already. There are many useful extensions ranging from extra browser security to developer tools. This is the browser I suggest for both Windows and Mac users. I personally use it as my main browser due to all the developer tools offered from third parties like Google.
In summary, I recommend Windows users to use a combination of IE and Firefox and I recommend Mac users to use a combination of Safari and Firefox. If you are a web developer I recommend installing IE, Firefox, Chrome, Safari, and Opera for testing your websites' compatibility across them all. I have also noticed on Windows that IE is less forgiving than the rest when it comes to malformed HTML and CSS. I often use it for debugging my webpages. Firefox should be your primary browser for web development due to the developer tools one can get for it.