You know, that's a good question given the threat exposure in a browser.
Maybe the right answer is a mixture. Use a dedicated Chromebook in guest mode for financial transactions/bill paying/banking (high security, low privacy from Google) and something akin to a text-based browser on an open source OS for everything else.
Is there something like Lynx but with a bit of formatting + still images? I can see going that route simply because the sheer size (in LOC) of a modern browser is so great that I question it's trustability.