Step 3: Password Database
I chose KeePass, which is free, open-source, and cross-platform, but you can use any similar program. KeePass is makes it easy open your banking websites and to paste your credentials into their browser login forms. There are also browser-specific plugins for even more convenience and all kind of other plugins, but I don't use any of them.
It's a bit confusing that there are two separate flavors, KeePass v1 and KeePass v2, and they are separate products. KeePass 2 has some extra security features to thwart keyloggers, but I use KeePass 1 because I couldn't get KP2 working on our Mac. Supposedly it is possible, but it wasn't important enough to me to keep trying.
For Mac and Linux, you use KeePassX, which is technically a different program, but is 100% compatible with the KeePass1 file format.
If you need to use this system on public computers like at the library or an internet cafe, then the extra security risk might prompt you to use KeePass 2 instead. You can't use the same database format with both programs, but you can convert back and forth if you really need to.