Dude, you want a proxy with different user ACLs. This is not a browser thing at all. 2 firefox profiles will do the same thing, each having a different proxy user set. Hell have 2 user accounts on your entertainment box, and ssh -X [EMAIL PROTECTED] when you want to bring up your secure account.
Keep the browser off the server box, instead put a filtering proxy of it. But hey its your life, do what you want.