Search
DuckDuckGo
Default in Tor and Brave. Search Engine that works and doesn't store your searches. Not fully Open Source. Gets money from un-targeted ads at the top of results.
Searx
Open Source and can be self-hosted. May not have as quality of results as some of the other providers.
StartPage
Also doesn't track you. Pays Google to use their search engine. Also earns its money from un-targeted ads (citation).
Ecosia
Ecosia's mission is to use the revenue generated by their ads and use them to plant trees. They proxy Bing search results. Has a minimal amount of tracking, but it respects Do Not Track requests.