I've never found a browser that does not leak some personal information. In most cases a few changes to the default configuration will plug most of the holes. Below are some tips for the Firefox browser, most of these measures can be used on other browsers, with Chrome being a notable exception...
Please Note: If you create master key systems for government installations or corporations who have tight security requirements, you should not be using a web browser for this, rather consider using a locally installed desktop software like MK Express.

1. In Preferences under Privacy:
  • Tell sites you do not want to be tracked.
  • Never accept thrid-party cookies.
  • Forget cookies when ever the browser is closed.
2. In Preferences under Search:
  • Change the default Search Engine to "DuckDuckGo" or "Startpage HTTPS".
  • Ensure search suggestions are NOT selected.
  • Deselect Bing, Google and Yahoo... or any other search engine involved with PRISM.
3. Install an extention like "Ghostery" and "Toggle Referer" to block the trackers.