Favorite buttons

I need to delete Favorites that pop up -- like Yahoo, Trip Advisor, Bing, etc. I don't want my homepage to be Amazon.com. I have cleared history until I'm blue in the face. I want to be able to edit those Favorites to reflect websites I use -- not those I don't use. This is a brand new iMac; not an iPhone. I just used an antivirus today and still can't get rid of Favorites. They're either buttons or a little list of stuff under the Search field. What in the **** do I have to do????????