Okay, some basic advice and knowledge.
- DuckDuckGo is fairly secure (https and all). They also claim not to store any personal data, so they're pretty good.
- Chrome is owned by Google and Google is not known for privacy. Google CAN see your searches in Chrome as well as all the pages you click on. Thus, I would suggest you switch to Firefox.
- Any site you go to can know that you did. They also can see that you came from DDG, but the CANNOT see what search you performed (they can with Google).
- Firefox also allows you to delete cookies from particular sites. This means that Google and other sites won't be able to link some data about you to other data about you that were recorded at different times.
- Try to use https://*
sites more than http://*
sites (means NSA can't peak so easily).
Your privacy on the web generally depends on how easy it is to compromise your privacy. The NSA can look decrypt your https connections, but it would take a lot of time, money and computing power. Thus, they'd have to be particularly interested in you. They can't do https decryption on everyone.