Not sure about where Opera stores it's cookies. They are readily available to edit or delete in tools, though.
Are you that worried about your security settings on your browser? I have been surfing the net for 5 years and never have been infected with a virus. Adaware, sure but they are not very difficult to get rid of.
I've been using Opera since version 5 something. Tried Mozilla but it worked better on Linux than windows for me. I say, try them all! Worst case scenario, you don't like them and remove them. In any event any one of them have got to be better than IE.
I just use my firewall program to block ads in my browser and use the "block unwanted popups" in Opera. No problems here.