I always use DuckDuckGo. It’s usually adequate, and certainly “the best of a bad lot”, if you want to look at it that way. I sometimes use bangs if I want to search directly on a site. For example, sometimes I’ll search for something like a code tutorial video directly from DuckDuckGo, and if I have trouble finding it, I’ll update my search to go directly to YouTube, e.g., “modern perl features” first, then “modern perl features !yt”.

I used to jump over to Google when I couldn’t find something through DuckDuckGo, but it’s such garbage now, I don’t even try. I haven’t used Google for months.

The last “tiny linux” that I used was BunsenLabs. That was for a netbook, though. No idea about Chromebook compatibility. https://www.bunsenlabs.org/