I've tried this but find it to quite a pain to remember what browser I should be looking at what in.
What I want is a browser where I can be logged into Google, and any link I click will open that link in my "private" (not logged into Google) browser. Same with Facebook, Twitter, etc.
So I've started developing XUL apps to run each in their own sandbox.
It's pretty simple right now. I only spent an hour or so on it and will post it to GitHub when I get some more time to iron out a few kinks.
Basically you open the XUL app for the service you want to access. It acts as a chromeless firefox browser and intercepts any links you click. If it's an external link it opens it in your default browser where you wouldn't be logged into google preserving a bit of anonymity.
I figure that keeping Google and Facebook in their own little prison should help greatly with privacy.
I use DDG for searching whenever possible.
Not so much to hide things (as a pastor I got used to being watched 24x7 years ago), but just to preserve what little privacy I have left.