In EU there are many price comparison engines with millions or billions of products. I don't know how popular they are. Some monetize trough ads, some have partnership with stores and you can buy directly from the search results.
I generally search first on the local Amazon equivalent, if I don't like what I see, I search on a smaller store. If I still can't find or dislike the products or prices I search Google. If I am still not contended with the results, I will go search on comparison engines.
And I also have a browser extension called Pricy who polls the comparison engines, so once I land in a product page I know which store has the better price and what was the price history through last year.
Probably many people have similar patterns. I expect people in US to search Amazon first, if it's not a very niche product they are after.
I think you can have a better monetization proposal, if instead of just search you build a sales platform, so people can directly buy after searching, without hoping to various websites.