Is it best not to use beta versions for online purchases/banking?
Simply put:-
If you use the Beta of Google Chrome to visit a webpage where someone has decided to exploit this bug for malicious purposes then it could have downloaded and installed anything it likes on your computer.
Sophisticated keyloggers, mouse position loggers, screen grabbers, network sniffers, zombie clients, etc.
Even if you then use IE, FireFox or Safari to connect to your webmail, online banking, work websites, etc the information could still be grabbed and uploaded to someone else.
However, you've still got to visit a dodgy webpage in the first place, but that's why nasty people spend a lot of time hacking legitimate websites (remember the ASSOS website was recently flagged as dodgy by Google) as they need as many people as possible to succumb to the original infection vector.
Personally I wouldn't touch it with a bargepole. If I did it'd be inside a handy VMWare "Scorched Earth" type sandbox.