The safest way that I know how to use the Internet & I do this when making transactions, is to run a Linux Live DVD. I have a Linux Mint 16 install DVD that is great for this purpose & since it runs from the memory after the fresh boot, any malware that could have been in memory is gone. That's assuming that I take care of my business & not doing a lot of browsing beforehand. Which is the main reason for this. Booting from a USB stick where persistence is enabled (your changes are saved) defeats that purpose. Though it's still quite good for many things.
One can do this with nearly any Linux OS that boots in Live or "Trial" mode. It's designed so that users can try the OS before install, but it serves for other purposes also, not only secure banking, but even resucing a Windows install under certain conditions.
The Live DVD is the only way that I know of for safe & secure Web browsing. Keep in mind though, your ISP still knows where you're traveling. This is for security, not total privacy, though unlike the installed OS, you shouldn't see a bunch of pop-up ads after using the Live DVD.
Hope this helps & Good Luck.