One other note, if your planning on doing any internet banking, your pretty much stuck with Firefox or Opera (using binary emulation). Haven't tried ie under wine on openbsd, it may work also.
Why? Because a lot of the internet banking sites are useless and while things like konqueror load them, badly hacked together js, and other bits fail a lot, things you won't notice until you go to do something like a funds transfer etc. You might be lucky and your banks website isn't ass. But I would be checking it thoroughly before making a browser decision. As for security, browser settings in such a way as to flush cookies at the end of sessions, clear cache etc and not store passwords is not a difficult thing, but in the end a scrubbing proxy would be a good idea if your uber paranoid.