Date: October 11, 2013 12:17AM
May I suggest some things that can help, but won't fix the router logging issue.
First, go to www.eff.org and install https everywhere. https://www.eff.org/https-everywhere-node
This will give you an encrypted connection between you and websites that offer it. Both your browser's requests and the pages you choose to display.
If any of your devices are shared, Firefox offers private browsing which keeps no cookies, or tracking information at all while it is on.
For absolutely private web browsing (this will fix the router logging issue) the only thing available is the Tor browser bundle. But, you will take a performance hit.
For web searches, use Duckduckgo and Blekko search engines.