2 GB for a frigging browser ? Dude... TinyCore Linux ! It should be enough to run just the browser. Also, there are LiveCDs (roughly 700 MB) that you can just fire up with VirtualBox, and even if they come with slightly outdated browsers it doesn't really matter that much. Malicious code will be contained within the virtual session (unless you set up shared folders or manually copy them to a flash stick, etc).
Here's an idea: Download the Kubuntu LiveCD, fire it up with VirtualBox and use Konqueror to browser the web. Why ? Because most exploits are tailored for popular browsers (IE, Firefox comes second, then there's Chrome, Safari, probably Opera somewhere in there too...). Konqueror can even impersonate other browsers using various browser id's in case a website is IE-only or doesn't let you in if it's not one of the "popular" browsers.
But don't get cocky. If the browser is compromised (and you won't even know if it does), all they need is your username and password. Heck, most people are dumb enough to use the same ones for more than one accounts (myself included, unfortunately). "Bulletproof" is more of an abstract concept, really. There's always the human element, which unfortunately is the weakest link.