How To Have The Best Security In Internet Banking?

As most of the people, I use internet banking.

Do you have any suggestions to have the most security in internet banking -

On my computers end (what software to use, how to, anti keyloggers, virtual pc, is it better or worse to use password software like lastpass? What usage habits?)

On banks end (giving access to my ip only (is this convenient?), changing mother maiden name regularly (is this legal? or what else can I change if it passes to other people?), limiting daily transfer and increasing by telephone when needed? and other suggestions.

On Modem?

How should I use the computer?

These might seem ridiculous to ask - but I believe every detail is important. I wait for your input and suggestions.

Edit: And what about this: can I install a linux on another partition, and use it for the banking - many malware are for Windows? Can this partition be encrypted and Windows on the other partition might not have access to it so malware can not spread? Or instead of linux, can I have a seperate windows partition invisible to the main Windows?

I will be using Internet Banking less frequently to be more secure.