The entire concept you're aiming to set up is terribly heavyweight and overkill. If you're knowledgeable enough to be discussing VMs and chroots, you must realize that what you are proposing is being careful to the point of paranoia à la tinfoil hat. Those of us who know how to stay as safe as possible via "basic" methods of security should be sleeping soundly knowing we're already in the top 5-10% of consumers. Install OS security updates, use a virus scanner and firewall, don't install pirated software (more likely to contain malware), and you're better off than most people by a significant margin.
You're talking about barely making a dent in the chances of your credentials or sessions being compromised. Private browsing, a separate browser instance, a VM, or chroot makes no difference if you have malware with a keylogger on the host system. Give yourself a break, realize that there is no such thing as "perfect security", and stop worrying so much. The amount of energy you're pouring into "banking safely" is not a sane endeavor. It serves no useful purpose. You could be investing this time and energy into something far more likely to improve your quality of life (eg: family, friends, health, etc.).