FixTracking.com lists plugins and settings you can use for your browsers to limit the ways people can track you, and shift your surfing to secure sites when and where available.
DuckDuckGo is itself a search engine that tries to stand out by embracing privacy as a feature. Further they don't have the implicit customization that might foster a filter bubble of only showing you results that fall within a narrow world-view. As an alternative they certainly seem worth experimenting with when you want to compare and contrast search results or just find an alternative to the other near-monopoly.
When it comes to browsing the web it is best to not keep all your eggs in one basket. For example the two browser approach involves having one for trusted web-sites only, and another for random web surfing. The trusted web browser has all your plugins enabled and settings rather lax, compared to the browser for surfing that has java, scripting, etc., disabled, and the settings locked down.
Though that advice may be a bit misleading, which is why the FixTracking site is worth a read, as some of the plugins and settings listed are worth exploring further.