I use Windows XP SP1 and IE6... I like to live on the edge.
Seriously though... there's no reason to believe that internet banking is any less safe than any other activity, and plenty of reason for the opposite to be true... primarily that in many jurisdictions, precedents have been set confirming the liability of the bank
in cases of internet fraud and identity theft.
Once your system is patched and you avoid the potential ingress of malware by not visiting dodgy sites or opening unsolicited mails, you are covering yourself as well as can be expected. If you want to be really careful, use noscript
with firefox to eliminate the possibility of script based malware ingress. You could also use an internet security appliance such as ipcop
to do border protection, intrusion/extrusion detection, malware scanning and so on.
As for which distro, they are all as good/bad as each other, but personally I like the Debian/Ubuntu family.