One of the most exploited methods of hijacking a computer is the running of malicious scripts through your web browser. Choosing a good browser can not just make your browsing more secure, but if you find one with a good set of features, can transform your whole experience. We does not make a blanket recommendation, but can point you in some good directions...
When Microsoft introduced their ActiveX technology in earlier versions of Internet Explorer, this opened up the possibility for website to run code on your computer. Since then, countless security patches and browser versions later, it is a lot more secure. In our opinion the safest way to browse the web is not to use ActiveX at all.
One way to ensure this is to use the Opera Browser, it has never and will never support ActiveX. There are now very few websites that require this technology any more, and for those few trusted (usually Microsoft) websites that do, one can always revert back to Internet Explorer.
Of course this doesn't guaruntee that nothing can get in through your browser, but it does significantly reduce the chances.
Mozilla Firefox, and the webkit-based browsers Google Chrome and Safari are also very good browsers; fast, and generally more secure than Internet Explorer.