The issue is today’s Web browser was never designed to be secure from the beginning. There is a large attack surface that has been exploited by many hackers. And it isn’t just the browser software, but a vast complement of add-ons such as Flash and plug-ins that are also full of weaknesses of their own, all of which require frequent patching. And firewalls can’t really protect all the Web traffic going to ports 80 and 443.
I think Chrome and Firefox are best towards that, they use a known security blacklist, and as least Chrome has a secure sandbox. Both have settings under advanced option that will let you turn on Malware protection. It really depends on the security settings you choose to utilizes, and how aggressive you want to be with it. I would still periodically scan your machine with antimalware such as Malwarebytes (free software you can get from https://www.malwarebytes.org/), as some stuff can still get through.
Take a look at this site, it covers details regarding security for different browsers: http://www.techsupportalert.com/content/how-harden-your-browser-against-malware-and-privacy-concerns.htm