You're on the right track. DuckDuckgo and Qwant are good options. Startpage used to be a good private search engine, but they were bought by System1, an advertising company, so that thing is doomed.
Originally Posted by lace
Privacytools.io has a small list of Privacy respecting search engines:
Also note that anonymous is different than private. If you want to be anonymous like Snowden, you'd need to up your game, ie, use Tor and tor search engines, along with Tails (a Gnu/Linux distro).