This depends on your definition of safe.
In terms of your computer being anymore safe from malicious attacks than it already is, would not be dependent solely on your search engine. Really, your search engine offers barely any protection at all against malicious attacks.
In terms of tracking, duckduckgo should offer you the most protection in this sense.
If anonymity is your goal, you will need to do more than just use duckduckgo. Google Chrome stores every page you visit, (unless in incognito mode I believe, and I wouldn't be foolish enough to believe it's true incognito). Your searches will all be saved in your browsing history. This isn't privacy oriented IMO.
So, if by safe you mean anon, you're definitely going to need to do some research, use a browser such as firefox, and start reading about browser config, because you will need to change a few settings ;)
Hope this answer helps!