A Searx instance could be a good compromise. Unlike StartPage, Searx is a meta search engine, i.e. it retrieves and processes results from various search engines.
Another important difference between the two is that Searx is free software and can be operated by yourself. DuckDuckGo and Startpage are proprietary software.
Welcome to searx. Searx - a privacy friendly, decentralized and non-commercial search engine. An interview with Adam Tauber, free software developer from Hungary.
https://netzpolitik.org/2018/interview-searx-the-web-search-engine-that-respects-your-privacy/