As a simple rule, whenever I want to search something and minimize polution to my web history, I open the other browser I never use and then go into incognito mode. As a side note, this reminded me of the "Neo looks for Morpheus" scene (the one just before "Wake up Neo").
But sometimes I can't find what I want in StartPage, so I added an extra button on StartPage to take me to the same search in Google (TamperMonkey script).