A basic usability test (very cheap also) is logging remote on another person’s computer and watching him/her use the app/website/tool. It’s eye opening.
So I have seen my mother (who is not a computer savy person) hovering the page in search of buttons. When she searches things she doesn’t use the keyboard, she presses the “Search” button, and when that’s not available she gets confused. If the search field has an arrow image background on the right side, she tries to click that arrow and gets puzzled when nothing happens.
So, please use search buttons.
Oh, and please don’t name them “Go” or “>>” or stuff like that, name them “search”, and even put a magnifying glass on them.