I've been using a local Searx[1] instance for web search for a few months now, and besides it needing an update when APIs inevitably break, it's been relatively pain-free. What I like the most about it is that I get a unified search results page for all engines, which avoids some of the profile bubble, and that the UI is always consistent, avoiding these scummy redesigns A/B tested to infinity and implemented because…
The anonymizing stuff searx does really seems to work. My search results seem uniformly neutral regardless of which computer/profile/browser is in use.
I host on my LAN and out on the WAN over https protected with simple auth. All my devices, including my work computers and cell phone browsers, are set to use it. I rarely end up on Google in my life.
I actually prefer its interface for everything but images (which are only OK, but still perfectly usable)