I've clicked X on the panels to remove the websites, though the panels are still there. How can I remove these panels completely when opening a new tab? Thanks.
Those panels show your recently visited / top visited sites. It's meant to be a convenient way to access them and it's the default behavior of Chrome's new tab page. You'll need an add-on to change it. There are a few available: https://chrome.google.com/webstore/search/new tab If you'd like to basically just have the Google Search when you open a new tab and no top sites, just download an add-on that will let you change the new tab page and make it the Google homepage.
Thanks for the suggestions. That would make for a lovely suggestion for the core of Chrome. I know in Firefox you can choose what you get when you open a new tab, and one of the options is a completely blank tab.