Mint was recently acquired by Intuit. How can I put this delicately? Lets just say it will be "interesting" to see what happens to Mint.com over the next year or so.
As far as not using Windows to access your bank data, good luck with that. While you might not use it your bank almost certainly does. Heck, I have even heard that a lot of ATMs and point-of-sale machines use XP. Some of the security breaches that article highlights were actually problems that originated at the bank, not the user's system.
If your system is infected with malware, I doubt a live CD is going to help. The bad guys will have access to your email account and that is probably enough to get the information they need. Plus, most people using a live CD will probably end up using simple, easy to remember passwords because the live CD won't save that data. Most will probably use a common password that they use on all their web sites which their malware infected PC has already supplied to the bad guys. Then there is the problem of incredibly slow boot times making the entire process a PITA.
I better recommendation than using a live CD would be to do all your online activity (web browsing/email) with a linux based virtual machine. VirtualPC is free, loaded it up with Ubuntu and you are all set.
A better recommendation even still is to take a little time to learn about computer security. Computers are powerful tools and if you don't learn to use them properly you going to have problems.
Some banks have two factor authentication schemes that help as well. For instance, with Bank of America, you can arrange it so that every time you try and access your account, B of A will send you a text message with a code (changes every login) that you also have to enter. So even if the bad guys had your name and password, they couldn't get in unless they had your cell phone.
An Apple machine is an option, at least for now (I use a MacBook myself). Although it may not always be. Of course, things like phishing scams work just as well on OS X users as Windows users.
-Keith