There is nothing that is 100% safe, as new threats appear all the time. Aside from using someone else’s computer instead of yours!
I would recommend Firefox with the NoScript add-on. This combination prevents many common problems (usually associated with Internet Explorer - I assume you use Windows) and in addition block malicious (or rather, all) javascript, which is a common vector for attack.
If you are really really paranoid and have not got access to (ab)use someone else’s computer, you could get hold of on of several Linux distributions that run as a stand-alone operating system on a thumb-drive.
Even if this was compromised - which is very, very unlikely - the damage would be limited to that OS, which could be overwritten if you realize there was a problem.